The effect of Large Magellanic Cloud on the satellite galaxy population in Milky Way analogous Galaxies

The effect of Large Magellanic Cloud on the satellite galaxy population in Milky Way analogous Galaxies

Dali Zhang, Yu Luo, Xi Kang
Purple Mountain Observatory, the Partner Group of MPI für Astronomie, 2 West Beijing Road, Nanjing 210008, China
School of Astronomy and Space Sciences, University of Science and Technology of China, Hefei 230026, China
E-mail:luoyu@pmo.ac.cn
Manuscript Version: Aug 2018
Abstract

Observational work have shown that the two brightest satellite galaxies, the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC), of the Milky Way (MW) are rare in the Milky Way analogs. It is then interesting to know if the presence of massive satellite have any effect on the whole satellite population in the Milky Way analogs. In this paper we investigate this problem using a semi-analytical model combined with the Millennium-II Simulation. The MW analogous galaxies are defined to have similar stellar mass or dark matter halo mass as the MW. We find that in the first case, the halo mass is larger and there are on average two times more satellites in Milky Way analogs if there is a massive satellite galaxy in the system. This is mainly from the halo formation bias. The difference is smaller if the Milky Way analogs is selected using halo mass. It is also find that the satellites distribution is slightly asymmetry, more concentrated on the line connecting the central galaxy and the massive satellite. We also find that on average LMC have brought in satellite galaxies with at its accretion, among which satellites are still within a distance of kpc from the LMC. Considering other satellite, we predict there are satellites with kpc from the LMC. By comparing our model to the early data of SAGA, a survey to observe satellite galaxy around 100 Milky Way analogs, we find that SAGA have more bright satellites and less faint satellites than our model predictions. Future comparison is needed for the final SAGA data.

keywords:
galaxies: halo - galaxies: Local Group - galaxies: dwarfs – Magellanic Clouds
pagerange: The effect of Large Magellanic Cloud on the satellite galaxy population in Milky Way analogous GalaxiesLABEL:lastpagepubyear: 2018

1 Introduction

The cold dark matter (CDM) model makes good predictions of the structure formation on large scales. However, on small scales the predictions are complicated due to the complex baryonic processes. Our Milky Way (MW) is the most well-studied galaxy in the universe(e.g. Bland-Hawthorn & Gerhard (2018)). In recent years, dozens of new faint satellites of MW has been observed (e.g., Koposov et al., 2015; Drlica-Wagner et al., 2015; Bechtol et al., 2015), therefore the whole member of MW satellites could be predicted more confidently (e.g., Trowland et al., 2013; Newton et al., 2018). The combination of satellite spatial distribution and kinematical properties (e.g., McConnachie (2018)) makes the MW to be an excellent local laboratory to constrain the CDM model and baryonic physics. For a recent review see Bullock & Boylan-Kolchin (2017) and Navarro (2018).

In fact, two well known problems have been found when comparing observation to theory. One of them is that the satellites predicted in CDM model are much more than what we have observed (the ”missing satellite” problem, Klypin et al. (1999); Moore et al. (1999)). The problem can be solved by suppressing the star formation rate in low mass haloes (e.g., Bullock, 2010; Maccio et al., 2010). The other problem is that the predicted central mass density is higher than observed (the ”too-big-to-fail” problem, Boylan-Kolchin et al. (2012). Several solutions have been proposed, such as the dark matter is not cold (e.g., Lovell et al., 2012; Vogelsberger & Zavala, 2013), the induced core from baryon physics and star formation (e.g., Brooks & Zolotov, 2014; Guo et al., 2015; Wetzel et al., 2016; Brooks et al., 2017), MW has a lower halo mass (e.g., Vera-Ciro et al., 2013; Dierickx & Loeb, 2017) or the MW has a particular favor of accreting its subhaloes (Kang et al. (2016)).

To solve these problems, searching more faint MW satellites is a major effort on one hand. On the other hand, it is equal important to search more MW analogs to identify if the MW is an outlier. A few studies have shown that the MW is not typical, especially in terms of its bright satellites distribution (Liu et al., 2011; Guo et al., 2011; Tollerud et al., 2011; Strigari & Wechsler, 2012). Considering the brightness of Large and Small Magellanic Clouds (LMC & SMC, with and ), studies found that 11% MW analogs contain an satellite like LMC or SMC, and only 3.5% of them contain both bright satellites (Liu et al., 2011). A similar conclusion is also made with simulation data (Boylan-Kolchin et al., 2009; Busha et al., 2011; Rodriguez-Puebla et al., 2013; Kang et al., 2016).

Considering the rarity of LMC like satellite in MW analogs, one important question is if the presence of a massive satellite, such as LMC, has any effect on the number and spatial distribution of the whole satellite population. In particular, does our MW contain more or less faint satellite galaxies than its analogs? If there are more satellites, how many of them are contributed by LMC? Answering these questions will shed light on our search of more faint satellites in the MW and the comparison with observations of the MW analogs. On the other hand, the effect of LMC like satellite on the whole satellite population may depend on how we define the MW analogous galaxies. Usually, the MW analogous galaxies is defined as a galaxy which has a dark matter halo similar to that of the MW, around . It is well known from the halo model ((Zentner et al., 2005; Deason et al., 2013; Mao et al., 2015)) that the number of satellite galaxies, as well as their mass distribution, are related with halo assembly bias. Lu et al. (2016) use an N-body simulation of Milky Way-mass halos with a fixed mass of to investigate the realtion between LMC and other satellites. They found that the presence of a LMC is correlated with halo assembly history, and different assembly history will have an effect on the number of satellites. Although using dark matter halo to define MW analog can be easily applied in simulation, for observational search of MW analogs, it is more straightforward to use the stellar mass or luminosity of the galaxy. SAGA (Satellites Aroud Galactic Analogs) Survey is an ongoing galaxy survey whose goal is to measure the distribution of satellite galaxies around 100 MW analogs own to (Geha et al., 2017). In their first phase of data, they have found 8 MW analogs and made some comparison between their samples and the Local Group.

In this paper, we investigate the effect of brightest satellite in the MW like galaxies using a semi-analytical model of galaxy formation. Although halo assembly is the main driver for the variance of satellites population in the galaxy, some physical effects will produce additional scatter, such as cosmic re-ionization, galaxy merger and tidal stripping. Semi-analytical model is able to include these physical process and our model (Luo et al. (2016)) have acquired much better convergence for simulation with different resolutions, which is essential for modelling the faint satellites of the MW. The goal of this work is to find out in which definition of MW analogous galaxies, the presence of a LMC-like satellite will affect the distribution of the whole satellite population. We introduce the data and our definition of MW analogous galaxies in Section 2. In Section 3 we show the satellite number and spatial distribution. In Section 4 we compare the model predictions with the recent SAGA results on the distribution of the bright satellites to identify if SAGA has missed some bright or faint satellites. We briefly discuss the results in Section 5.

2 Methods

Figure 1: The distribution of , the gap between the stellar mass of central galaxy and the most massive satellite, in central galaxies in different mass bins. The black dash line is the value of for the Milky Way.

In this work, we use the semi-analytical galaxy formation model of Luo et al. (2016) implemented on the Millennium-II simulation (MS-II, Boylan-Kolchin et al. (2009)) to produce model galaxies. The original MS-II simulation is a dark matter only cosmological simulation with particles in a cube box with each side of . After rescaling the cosmological parameters from the WMAP1 to the WMAP7 cosmology (a method developed by Angulo & White (2010)), the box size of MS-II is rescaled from to , and the mass of each particles are changed from to . It is shown that such a simulation has enough resolution to resolve faint satellite down to (Guo et al., 2015). The semi-analytical model of Luo et al. (2016) is a resolution independent model based on the Munich galaxy formation model: L-Galaxies (e.g. Kauffmann et al., 1993, 1999; Springel et al., 2001; Croton et al., 2006; De Lucia & Blaizot J, 2007; Guo et al., 2011, 2013; Fu et al., 2010; Henriques et al., 2015). For more detail about the models, we refer the readers to these references.

In the L-Galaxies model, galaxies are classified into three types. Type 0 galaxies are those located at the center of Friends-of-Friends (FoF) halo groups, and we take these galaxies as centers (host galaxies) of these groups. Therefore, there is only one type 0 galaxy in each FoF group, and in most cases, the type 0 galaxy is the largest and the brightest member of the group. Both type 1 and Type 2 galaxies are regarded as satellites galaxies in the model. A type 1 galaxy is located at the center of a subhalo, which is an overdensity within the FoF halo (Springel, 2011). The halos / subhaloes contain at least 20 bound particles for Millennium-II (Springel, 2011; Boylan-Kolchin et al., 2009). Type 2 represents the orphan galaxy without resolved subhalo and it is usually the descendant of a Type 1 galaxy.

In the literature the most common way to define the MW analogous galaxies is using the dark matter halo mass. Great efforts have been devoted to measure the dark matter halo mass of the MW and most results lie between and , but most concentrate at around (Li et al. (2018); see Callingham et al. (2018) and Wang et al. (2015) for a summary of different methods and results). In our work we use two selection criteria to select MW analogous galaxies. The first one is the virial halo mass and we select those with virial mass between and as the MW analogs. The second one is to use the stellar mass of the central galaxy. In the SAGA survey, Geha et al. (2017) define the MW analogous galaxies using the K-band luminosity of the central galaxy and they obtained MW analogs with using the abundance match method, which is slightly larger than the reported K-band luminosity of the MW in the literature (e.g.,Klypin et al. (2002)). This luminosity range roughly corresponds to stellar mass between and . In this work we also use this stellar mass range to select the MW analogous galaxies partly for comparison with the SAGA results. For satellite galaxies, we use a -band magnitude cut with considering the resolution of the simulation.

To investigate the effect of a massive satellite galaxy on the distribution of the whole galaxy system, we use the gap in stellar mass between the central galaxy and the most massive satellite, defined as , to quantify the resemblance to the MW. Here is the stellar mass of the central and the most massive satellite galaxy. The MW have a stellar mass of and LMC have a stellar mass of , thus we use as a standard to split our MW analogs into two classes, with one class contain a large satellite and the others do not.

Figure 2: The Stellar mass-halo mass distribution of center galaxies in our model. The upper-left panel is the distribution of all the galaxy samples in the model, along with the relations from the abundance matching by Learthaud et al. 2011 and Moster et al. 2009. The upper-right panel is the distribution of galaxies with , and the blue solid and dashed lines repsent the median value and 1 deviation region. While the bottom-left panel is the distribution of galaxies with . The comparsion of these two samples are shown in the bottom-right panel.

3 Results

3.1 how does the LMC affect the satellite mass distribution

In this section, we investigate the distribution of and its impact on the stellar mass-halo mass relation, satellite number/spatial distribution.

We firstly show the distribution of in Fig. 1. We select central galaxies in three mass bins and plot their PDFs of . The vertical dashed line is the of the MW. It is seen that for small galaxies, the gap is larger, while for massive galaxies the gap is smaller, in consistent with that of Kang et al. (2016). As the subhalo mass function (normalized by the host halo mass) is very weakly dependent on the host halo mass (e.g., van den Bosch et al. (2006) ), it is interesting to ask why the gap in stellar mass has dependence on the central stellar mass or the host halo mass. This is mainly because the star formation in low-mass galaxies decreases rapidly (Guo et al., 2011), leading to large gap in stellar mass for given gap in dark matter mass. The plot shows that for the galaxies with mass less than MW (), the peak of distribution is larger than 1.6, while for the galaxies with stellar mass larger than MW, the peak value of is lower than 1.6. It means that whether a galaxy group contains a LMC-like satellite is correlated with the mass of the central galaxy.

In Fig. 2 we check the stellar mass-halo mass relation for central galaxies in our model. The upper left panel is for all central galaxies with stellar mass between and , and the lines show the relation from the abundance matching by Moster et al. () (2009, red line) and by Leauthaud et al () (2011, blue line). The upper right and lower left panels for central galaxies with larger/smaller gap. The lower right panel compares the median relations for the two samples. The upper left panel shows that our SAM galaxies roughly agree with the abundance matching results, indicating that the model parameters are correctly tuned. The lower right panel shows that at given stellar mass, a galaxy with lower tends to have a larger virial halo mass, which is easy to understand since both and halo mass are affected by halo assembly history. Such a trend is stronger in massive galaxies.

As the halo virial mass of a galaxy is a more physical property, it means that the presence of a massive satellite might have an effect on the whole satellite population. In Fig. 3 we plot the dark matter mass function, stellar mass function and luminosity function of the satellites. In the left column galaxies are selected by the stellar mass, i.e, the MW analogs are selected with stellar mass in the range of and . In the right column, MW analogs are selected using the halo virial mass in the range of and . In each panel the red lines are for galaxies with lower and blue ones for those with larger . As this selection is based on the massive satellite galaxy, which will then introduce a bias at the massive end of each panel, so we do not count the most massive satellite galaxy in the sample with lower and only show the mass functions of all other satellite galaxies.

From Fig. 3 it is found that by selecting the MW analogs using the halo virial mass, the satellite galaxies distributions have no dependence on except at the very massive end, i.e., the presence of a massive satellite, such as LMC, has no effect on the total and luminosity distribution of other satellite galaxies. However, if we select MW analogs using the stellar mass of the central galaxy, the presence of a massive satellite will lead to more satellite galaxies around the galaxy (left column). The left column shows that the total number of satellite galaxies will increase by a factor of 2 compared to those with larger . This is mainly due to the result that galaxy with lower have larger halo mass. Such an effect is significant and could be verified using large survey of MW analogs, such as SAGA with full coverage of its 100 galaxies. We will briefly compare our model predictions with the early results of SAGA in Sec.4.


Figure 3: The satellite mass and luminosity distribution in MW analogs. The samples selected by stellar mass of central galaxy are shown in the left column, and the samples selected by halo virial mass are shown in the right column. The upper two panels are for satellite halo mass and stellar mass, lower panel for satellite luminosity. The red line represents the samples with , blue line represents the samples with . The dash lines represent 1 deviation. The vertical dashed lines ( ) in lower panel are shown resloution limit of our model.

3.2 Satellite Spatial Distribution

In previous section, we find that the presence of a massive satellite will lead to more satellite galaxies around the galaxy selected by stellar mass. Here we investigate if the radial and angular distribution of the satellites will be affected by the massive satellite. We show the center-satellite distance distribution in Fig. 4. In the upper panel the contour shows the distribution, while black line shows the average distance. In the bottom panel, we show the satellite distance distribution function in unit of the virial radius. The dashed lines show the 1 variance. It is found that when a galaxy system have a lower , more satellites are likely to stay slightly far from central galaxy, and the average distance to the central galaxy is also larger.

We also show the angular distribution of the satellites in Fig. 5. We define to describe the angular position of satellites respect to the largest (ie. the most massive) satellite, and the configuration of is shown on the top panel. The distribution of average value of cos is shown in the middle panel. As we can see, for larger value, the average value of cos is close to . The average value of cos tends to be larger when decreases, which means the angular distribution of all the satellites are affected by a large satellite, with more number of satellites located at the same side with the largest satellite. We show the angular distribution of two samples in the bottom panel. The angular distribution of satellites shows some kind of elliptical, with more satellites stay at the position with cos, especially for the galaxies with lower . For MW-like samples, we limit its in a narrow range with , about 9% of the satellites stay in a narrow cone on the orientation of the largest satellite (cos 0.9).

What leads to the slight larger distance and more narrow angular distribution of the satellite galaxies if there is a massive satellite, such as the LMC? One possible reason is that the most massive satellite is recent accreted and is still orbiting at the outer halo region of the central galaxy. As massive satellite galaxy may have its own satellite, i.e., satellite of satellite, these satellites are still concentrated around the massive satellite, then leading to a slight larger distance and angular distribution towards the massive one. Another possible reason is that there is a low potential region between center and the largest satellites because of their gravity, some of the satellites are trapped in the low potential region.

Figure 4: The central-satellites distance distribution with . The upper panel is the distribution of average center-satellites distance with respect to , where the distance is normalized by halo virial radius. The black line is the average value of the distribution with error bar representing deviation. The bottom panel shows the PDF of the distance in two samples, dashed lines represent 1 deviation.
Figure 5: The angular distribution of satellites with respect to the largest satellite galaxy. The upper panel illustrates the configuration of angular position of satellites. Cent means center galaxy, and represents the largest satellite, means other satellites. In the middle panel, contour plot represents the distribution of , with the average value of the contour and 1 deviation shown by black line with error bar. The bottom panel shows the angular distribution of satellites in two samples.

3.3 Satellites in Neighborhood of LMC

So far, more than 50 Milky Way satellites has been detected, and 13 of them are locate within 50 kpc of LMC (Koposov et al., 2015; Bechtol et al., 2015; Drlica-Wagner et al., 2015; Homma et al, 2018; Kim & Helmut, 2017). In this section, we will investigate the satellites in the neighborhood of LMC-like satellites and satellites of LMC analogs before their accretion. In last sections, we select the satellites in our model with a magnitude cut of considering the resolution limit (see bottom panel in Fig. 3). While in observation, 12 of 13 satellites in the neighborhood of LMC are faint with , except SMC (). In this section, we change our magnitude cut to to make a prediction of satellites nearby LMC. Here we note that our model predictions for the very faint satellites may be affected by simulation resolution.

In the CDM scenario, satellite galaxy is the remnant of a merger event. For each halo in our model, we traced its massive satellite, labeled as , back to the snapshot before it is accreted. In that snapshot, was central galaxy in its own FoF group, with numbers of satellites in that halo. After merged with a massive galaxy, its satellites become satellites of the new central galaxy and some of them have merged with the central, others are survived.

In this section we investigate the infall time of and the fate of its satellite galaxies after is accreted. We also record a merger time, labeled as the largest merger time of the halo, in which the merger event contributed the most number of satellites. In Fig. 6 we show the distributions between the infall time of , the largest merger time and the gap . From the left lower panel, it is found that there is a correlation between infall time and , such that the satellite is massive, the later is the merger event. This is reasonable as the dynamical friction time is short for massive satellite galaxy, so its presence indicates a very recent merger. The upper right panel shows that there is a very good correlation between the infall time of and the largest merger time, indicating that usually the most massive satellite contributes the most number of satellite galaxies. The upper left panel is the relation between the largest merger time and . We use the largest merger time as a tracer to indicate the formation time of the galaxy. When to be smaller, the largest merger time tends to be later, which means the value of a galaxy is correlated with the history of halo accretion. Some investigates (e.g., Zentner et al. (2005)) have shown the gap between main halo and the largest halo is related with halo assembly history, which is the main dirver for the gap in stellar mass between galaxies. However, there is some different between galaxy gap and halo gap, since some other processes, such as cosmic reionization and galaxy merger, might also make some contribution. We have shown in Fig 2 that for same stellar mass of the center galaxy, the halo mass tends to be larger when the galaxy have a smaller value, suggesting that the deviation of halo mass is correlated with halo assembly history. Lu et al. (2016) have shown that the galaxies with slower accretion ratio have a larger central galaxy, considering the relation between halo assembly history and .

Now we check the fate and origin of the satellites around . We classify the satellite galaxies in each halo into three classes, . Class represents all satellites which were satellites of before accretion and have survived until present, ie, they are still satellites in a galaxy group while not merged into other galaxies. Class are the neighbor satellite of , where we define the neighbor as those within a distance of 50 kpc from . Class are neighbors of and they were once satellites of before accretion.

Figure 6: The relation between merger time and . The largest merger is defined as the time of merge event which contributes the most number of satellite galaxies. The upper-left panel shows the distribution between largest merger and , and the bottom-left panel shows the distribution between the infall time of and . Both merger time of and largest merger present a correlation with . The right panel shows the relation between the time of largest merger and infall time of , which indicates that in most cases the galaxy (most massive satellite) contributes the most number of satellites during its accretion by the host galaxy.

In Fig. 7 we show the properties of the satellite associated with . Note that here the x-axis is the stellar mass of the massive satellite, labeled as . The upper left panel shows the average distance between the largest satellite and class a satellites. The average distance spread from dozens of kpc to hundreds of kpc, and shows no significant correlation with mass of the largest satellite. The average distances is the order of the virial radii of the host halo, which means that after infall, most of the satellites of escaped from , and become satellites of center galaxy. The lower left and upper right panels show the number of class and class satellites, labeled as and . They show that both and are well correlated with the mass of , indicating that more massive satellites have brought more satellites when they infall, and may keep more of these satellites to its neighbor for a long time till now. The bottom right panel shows the number of class - distribution. There is no strong correlation between and , showing that the number of satellites in neighbor of could not be predicted by the mass of only.

Fig. 7 is for all MW analogs with stellar mass between and . If we further limit the LMC analogs mass as , we found that there are on average satellites which were the satellites of LMC before infall into MW, and satellites still stay in the neighborhood of LMC, others are stripped and distributed with a distance larger than kpc to the LMC. If we use the satellite magnitude cut as to select our samples, we find that there are on average satellites which were the satellites of LMC before their infall into MW, and satellites still stay in the neighborhood of LMC with . Dooley et al. (2017) and Shao et al. (2018) also obtained similar conclusions with ours.

Figure 7: The distribution of satellites with affiliated with (the largest satellite). Subscript a represents satellite-of-satellite, which means they were in a same FOF group with before is accreted by the host galaxy, subscript b represents satellite-of-satellite in neighbor (distanse 50 kpc) of , and subscript c represents neighbor of . These satellites are represented with (, ) respectively, while (, ) represents the number of (, ). Here means the average distance between and . We find that tends to have a value of 50 kpc, which means most satellites of are escaped from its neighbor. Both and have good correlations with , while shows no correlation with .

To make a prediction about the neighbor satellites around the massive satellite , in Fig. 8 we show the relation between the number of satellites within kpc of and the distance between the massive satellite and the central galaxy, . Here we show the results for which is in different mass bins. It is shows that for larger than , the number of satellites is slightly larger than the numbers in other mass bins, which means the mass of has some effect on the number of neighbor satellites. For LMC like satellites (the black lines) or satellites smaller than LMC (blue and orange lines) , the difference of the number of neighbor satellites is much smaller, while the distance to the central galaxy has a dominant effect on the number of neighbor satellites. We predict from this panel (black line) that satellites with should been observed within 50 kpc of LMC. If we change the magnitude cut to , there is satellites.

In reality, LMC has only 1 satellite with (SMC, with ), and 13 satellites with within kpc. Compared with model, there is more faint satellites and less bright satellites observed around the LMC. One possible reason is that the resolution of the simulation we used, MS-II, is still too low, which is not able to resolve and trace the very low mass halo and subhaloes. In addition, in the model we do not consider the stripping of the satellite stellar mass, so the model may over-estimate the number of bright satellites.

Figure 8: The relation between the number of neighbor () around and the distance () between central galaxy and the most massive satellite . Here we show results for in four mass bins. The black line with errorbar shows the case for with mass similar to LMC.

4 Comparison with SAGA

SAGA aims to measure the distribution of satellite galaxies up to the luminosity of Leo dwarf () in around 100 MW analogs (Geha et al., 2017). It has published the early results for 8 galaxies. They found that there is a large scatter between the 8 galaxies, and in general, the observed satellite luminosity function has a flatter distribution compared with the prediction. Still there is a missing satellite problem with more faint satellites not observed. In this section we compare their results with the predictions from our semi-analytical model. Note that here we select MW analogous galaxies using the stellar mass of central galaxy with the same coverage as SAGA, as introduced in Section.2.

In the first release data of SAGA, the 8 galaxies have 27 satellites in total, among them one galaxy has 9 satellites, 4 galaxies have only two satellites, thus the satellite luminosity function of each galaxy has larger scatter and depends on the host luminosity. Here we combine the total satellite of the 8 host galaxy and plot the luminosity function using the magnitude difference with the host. This will eliminate the dependence on the host luminosity. In Fig. 9 we show the satellite luminosity function as a function of , where , is the r-band luminosity of the satellite and the host galaxy.

Figure 9: Satellite luminosity functions in observations and the model. The upper panel is for all central galaxies with stellar mass similar to the MW. The lower panel is for those central galaxy containing a massive satellite. The black dashed lines show the deviation of the Luo16 model predictions. It shows that SAGA and MW have similar distribution of bright satellites, but MW has more faint satellites. The model contains more faint satellites than the data, while the predicted number of bright satellites agrees with the data if the existence of a massive satellite is considered (lower panel).

The upper panel of Fig. 9 shows that in general the satellite luminosity of the MW is consistent with our model prediction, indicating that the SAM (Luo et al., 2016) have correctly captured with the physics of galaxy formation on small scales. This is not surprising as the model is based on the L-Galaxy model (e.g., Guo et al. (2013)) which have tuned the model to fit the galaxy stellar mass function up to very faint end. The satellites distribution from SAGA is very similar to that of the MW except at the faint end where SAGA has less faint satellites. Compared with the SAM prediction, both SAGA and MW have more bright satellite galaxies, but SAGA have less faint satellites than the predictions. One might reason is that SAGA missed some of the faint satellites, which may be due to their observational strategy. On the other hand, our model might have something incorrect, which means some phenomenon in observation are not well reproduced, such as missing satellite problem.

In the bottom panel of Fig. 9, we plot the distribution of samples with . We find that once we compare SAGA & MW satellites distribution with the samples which contain a large satellite, the model agrees well with observation data at bright end, while model shows more satellites on the faint end. This indicates it should not be neglected the contribution of the most massive satellites when we define MW analogs with stellar mass selection.

Now we further check if the distribution of the brightest satellite in SAGA is consistent with the model prediction. In upper panel of Fig. 10 we show the relation between the and the stellar mass of the central galaxy. The black diamonds represent SAGA galaxies, and black stars for MW and M31. It is seen that there is a weak trend that larger central galaxy have a smaller , consistent with the result in Fig. 1. Compared with the model result, most SAGA have a smaller , also consistent with that of MW and M31. From Section.3, we have found that the stellar mass-halo mass relation is dependent on the stellar mass of central galaxy and .

Then we estimate the deviation between SAGA and our simulation samples. Here we only count the number of satellites, , with according to the magnitude limit of SAGA. In the middle panel of Fig. 10, the colored contour shows the distribution of for all model galaxies regardless of their . The SAGA galaxies seems have similar satellite number as the model prediction, but we notice all the SAGA galaxies have smaller than most of the model galaxies (see the upper panel of Fig. 10). Therefore considering the effect of the most massive satellites as discussed in Section 3, the SAGA galaxies may underestimate the number of their satellites. Then we select central galaxies covering the same stellar mass and as the SAGA galaxies, roughly correspond to the region covered by the white lines in upper panel of Fig. 10. The expected number of satellites is shown in the lower panel of Fig. 10. It is seen that both the satellite number of MW and M31 are consistent well with our model, but the SAGA galaxy have a deficit of about 2 satellites on average per host galaxy. As previous shown, the satellites produced in our model, which not been found in observation should be faint, close to the detection limit of .

Finally we note that SAGA currently has only satellite data for 8 galaxies, as also mentioned by their paper (Geha et al., 2017), the sample size is still too small. With more data available in future, the satellite luminosity function can be measured more accurately and comparison with the model will be more reliable.

Figure 10: Upper panel: the relation between the mass gap () and the stellar mass of the central galaxy. Lower two panels: the number of bright satellite galaxies (down to ). The color contours show the distribution of the model galaxy. Black diamonds represent 7 of the SAGA galaxies, and black stars represent MW and M31. The upper panel shows that the SAGA galaxies and MW have lower compared to the model galaxy with similar central stellar mass. However, considering the SAGA galaxies have lower , the bottom panel shows the expected number of satellites from model galaxies selected with similar stellar mass of central galaxy and (the region shown by the white lines in upper panel).

5 Conclusions & discussion

Both observational and theoretical studies have found that the Milky Way is atypical that it contains more bright satellites, such as LMC and SMC, than the MW analogs. In this work we use model galaxies from a semi-analytical model combined with high-resolution N-body simulation to study the effect of the largest satellite in a galaxy system on the whole satellite population. Particularly, we select the Milky Way analogous galaxies in our sample and investigate the effect on the satellite number density and spatial distributions when there is a LMC like satellite. Our results can be summarized as follows:

  • By selecting the Milky Way analogs using the stellar mass of the central galaxy, we find that galaxies with a LMC like satellite have larger dark matter halo mass and more satellite galaxies than those without a LMC-like satellite. The difference disappears when the Milky Way analogs are selected using the halo virial mass. We also find that the gap between center and the largest satellite is correlated with the largest merger time.

  • The space distribution of satellites tends to be slightly away from the center galaxy and to be asymmetry with more satellites concentrated on the line between the central galaxy and the largest satellite when there is a large satellite. The degree of anisotropy is correlated with the mass of the largest satellite.

  • The large satellite is accreted into the Milky Way more recently, and it brings more satellites if its mass is larger. It is found that LMC have brought satellites with into the Milky Way, and there are about satellites still staying in the neighborhood with distance kpc from LMC. Others have been scattered into the Milky Way halo. Considering the contribution of satellites not from the LMC, we predict there are on average satellite galaxies within a distance of kpc from the LMC. This number is less than what observed around the LMC (13 satellites). We note that the simulation we used has no high enough resolution to resolve and trace the very low-mass haloes and subhaloes. Thus a further study using higher-resolution simulation is called.

  • When comparing the early data from SAGA to the Milky Way and the model, we find SAGA have similar distribution of bright satellites as the Milky Way and our semi-analytical model, and have less faint satellites than our model. On the one hand, we suggest that the deviation between SAGA and our model might due to their observation techeniche, which means SAGA is focusing on finding bright satellites. On the other hand, the deviation might due to the inaccurate of our model. However, the conclusion should be taken as caution as there are currently satellites data for 8 galaxies from SAGA, and more comparison is needed after it finishes the survey for about 100 Milky Way analogs.

We select the MW analogs containing a LMC-like satellite, and predict the number of satellites in the neighborhood of LMC-like satellites. While in the true MW system, LMC and SMC stay very close to each other, and each of them has their own small scale satellite system. LMC and SMC might affect each other and the satellites around them may be influenced by these two big members, which might make the satellites distribution deviate from our prediction. Besides, other properties, such as the shape and color of the central galaxy, the large-scale environment, etc. might also influence the satellite distribution, which is not included in this work. We believe further high-resolution hydro-dynamical simulation of MW analogs will be ideal to study the satellites around the LMC and SMC.

Acknowledgments

The Millennium-II Simulation databases used in this paper and the web application providing online access to them were constructed as part of the activities of the German Astrophysical Virtual Observatory (GAVO). We thank the anonymous referee for valuable suggestions on the paper. This work is supported by the National Key Basic Research Program of China (2015CB857003), the NSFC (No. 11333008, 11825303, 11861131006, 11703091). We thank Qi Guo and the members in our labotory for useful discussion.

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