Tracking the evolution of satellite galaxies: mass stripping and dark-matter deficient galaxies

Among the main properties of galaxies, the half-mass radius provides valuable information on the galaxy formation and evolution process, while DM halo mass is linked to the assembly history of their hosting haloes. The halo mass – galaxy size relation was investigated for central and satellite galaxies separately in Rodriguez et al. (2021). At redshift $z=0$, the results reported in that work indicate that, both in observations from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7; Abazajian et al., 2009) and simulations from TNG300, the size of central galaxies increases with halo mass, while the mean size of satellite galaxies depends only slightly on the mass of their host halo. In this section, we extend this analysis by addressing the redshift evolution of the halo mass – galaxy size relation for satellites in TNG50, TNG100, and TNG300. Our analysis provides insight not only on the physical processes that shape the evolution of satellites, but also on the effects of resolution and volume on the measurements.

In Fig. 2, the halo mass – galaxy size relation is displayed for satellite galaxies at four different redshifts ($z=0.0,0.5,1.0,2.0$, respectively) for TNG50, TNG100, and TNG300. In order to follow up on the Rodriguez et al. (2021) work, we have employed the size determinations from Genel et al. (2018), which are available for the aforementioned redshifts. In particular, the relation is measured using the 3D half-mass radius. Details on the measurements and selection criteria, which dictate the lower halo mass limits in Fig. 2, can be found in Genel et al. (2018)²²2We have checked that the mass –size relation does not change significantly when the standard TNG size measurements are employed.. Generally speaking, Fig. 2 confirms the results reported in Rodriguez et al. (2021) at $z=0$, showing little dependence of the size of satellites on the mass of their host haloes, even when different redshifts and boxes are considered. Some exceptions to this general trend are, however, noticeable. For a given box, the most relevant deviation is apparent for TNG50 at low halo masses, where the average half-mass radius drops significantly at all redshifts (at very small masses it goes up again). This seemingly erratic behaviour is relatively surprising, since TNG50 is by construction better equipped to deal with small haloes. Note that these are all haloes that are above reasonable resolution thresholds.

Clearly more significant than the above deviations is the dependence of the average size of satellites on the box employed, and, thus, on resolution and volume. As resolution decreases with volume, the average size of TNG galaxies increases, with differences between boxes of the order of $\sim 0.2$ dex. This behaviour was expected from the results shown in Fig. 1. It has also been documented before in the literature (stellar mass from TNG300 and TNG100 is typically rescaled by a factor of $\sim 2$, and $\sim 1.5$, respectively, see e.g. Vogelsberger et al., 2018, 2020; Engler et al., 2021). Continuing with the discussion on the mean size of satellites, the redshift evolution predicted by different boxes seems to be slightly different as well. While in TNG300 satellites are on average smaller at higher redshift, this effect is not as clear in TNG50 and TNG100. Again, these different behaviours are seemingly related to the different populations mapped by the boxes.

Despite the aforementioned differences, there is not a strong case for a dependence of galaxy size on host halo mass for satellites, independently of the redshift considered. This result is not obvious. On the one hand, more massive haloes could be more likely to accrete larger galaxies, which could potentially imprint a dependence on halo mass. Of course, the picture is complicated by the physical processes that take place inside haloes. Mechanisms such as mass stripping play a key role in the dynamical evolution of satellite galaxies. Despite this complexity, the absence of any significant correlation between their sizes and the properties of their hosting haloes is an important result.

Finally, we have checked that the differences between boxes manifest themselves also at fixed stellar mass. The stellar mass-size relation displays a higher amplitude in larger boxes (with variations that depend on stellar mass). At fixed stellar mass, there is a higher fraction of large galaxies in TNG300 as compared to TNG50. This might in principle have an impact on the amount of mass stripping predicted by each box (more extended disks could be more sensitive to stripping). As we will show in the following sections, this effect is, however, not noticeable in the mean evolution of satellite galaxies.

There is a tight physical connection between the properties of satellite galaxies and the properties of their subhaloes. In this section, we explore this connection by measuring the evolution of the stellar-to-(sub)halo mass relation (SsHMR) for satellite galaxies. These results (i.e., the ratio of stellar mass to subhalo mass as a function of subhalo mass) are presented in Fig. 3 for the three TNG boxes. Note that subhalo mass includes all material components.

The intrinsic differences in the population of subhaloes mapped by each box have again an impact on the SsHMR measurement, despite a general, qualitative agreement. For all boxes, haloes above a certain mass seem to display a relation that resembles in shape that measured for central galaxies (see, e.g., Behroozi et al., 2010), including the characteristic peak of galaxy formation efficiency. This is in agreement with previous findings from Engler et al. (2021). The subhalo mass of the peak seems consistent for different boxes and redshifts, although the peak mass fraction is larger for the smaller boxes (note that TNG50 does not reach high host halo masses with enough statistics, so the subsequent drop is not observed). The characteristic mass above which the SsHMR behaves like that of centrals varies from box to box, ranging from $\log_{10}M_{\rm host}[{\rm M_{\odot}}]\simeq 11$ in TNG300 to $\simeq$10 in TNG50 (with some redshift dependence). In Fig. 3, we show the number of DM particles that correspond to these thresholds.

Below the characteristic mass, and particularly for low redshifts, a significant enhancement in the fraction is observed. This increase in the stellar mass of subhaloes is attenuated as we move to higher redshifts; at $z=2$, no enhancement is observed. One possibility is that the effect is completely unphysical and caused by resolution issues (in Engler et al. 2021, the range of subhalo masses is restricted to $\log_{10}M_{\rm host}[{\rm M_{\odot}}]\gtrsim 11$). At faced value, however, there are physical effects that could explain the trends. First, we will show in following sections that lower-mass subhaloes (particularly in low-mass host haloes) lose DM material more easily due to mass stripping. Stripping would also affect the stellar component, but in a lesser extent since this is more concentrated inside the potential well of the subhalo (e.g., Smith et al. 2016). This would explain the fact that the enhancement becomes stronger at low redshift (since subhaloes would have been exposed to mass stripping for a longer period of time). Second, the resolution cuts that we impose, which run diagonally on the $M_{*}/M_{\rm sh}$ vs. $M_{\rm sh}$ plane, would tend to amplify the effect on the average $M_{*}/M_{\rm sh}$ fraction, perhaps artificially. This, in combination with the resolution itself, would explain the fact that the subhalo mass at which the enhancement becomes significant decreases for smaller boxes. It is important to stress that the low-mass enhancement occurs in TNG50 at subhalo masses that appear to be sufficiently well resolved (e.g., $\simeq 7000$ DM particles at $\log_{10}(M_{\rm sh}[{\rm M_{\odot}}])=9.5$). We have also checked that a more restrictive stellar mass resolution cut does not eliminate the feature.

There is little discussion on the SsHMR in the literature. In Engler et al. (2021), the relation is measured and discussed in detail for the TNG boxes for subhaloes above $\log_{10}(M_{\rm sh}[{\rm M_{\odot}}])=10.5-11$. Importantly, they compare the SsHMR of satellites and centrals, showing that, at fixed stellar mass, the former is shifted towards lower dynamical masses. This effect is attributed, again, to tidal stripping of the DM component working outside-in inside the subhalo (Smith et al., 2016). In Fig. 3, we explicitly compare our results with those presented in Zhang et al. (2021), where galaxies from the SDSS are linked to subhaloes from the ELUCID simulation. The SsHMR from Zhang et al. (2021) decreases with host halo mass from $\log_{10}(M_{\rm sh}[{\rm M_{\odot}}])=11$, the lowest halo mass considered. Unlike for TNG, there is no peak or plateau in the SsHMR of Zhang et al. (2021) within the halo mass range considered.

The scaling relations presented for satellite galaxies reflect the intrinsic link between the baryonic and DM components of haloes in the TNG boxes. In the next section, we will address in more depth the individual evolution of subhaloes harbouring satellite galaxies to evaluate the effect that mass stripping has on their material components. To avoid potential resolution issues, we will restrict the analysis to satellites in host haloes with masses above $\log_{10}(M_{\rm host}[{\rm M_{\odot}}])=11$.

As galaxies fall into groups and clusters, they experience a variety of physical processes that can alter their structure and matter content. In particular, processes such as tidal stripping result in varying degrees of mass loss, including stellar, DM, and gas mass. It is also well documented that both tidal and ram-pressure stripping can produce the reduction and even truncation of star formation (e.g., Fillingham et al. 2016, 2018; Simpson et al. 2018). One of the main goals of this paper is to quantify the combined effect of different mass-stripping mechanisms in the TNG boxes. It is important to emphasise again that the TNG boxes map intrinsically different satellite galaxy populations due to the differences in box size and resolution (see Fig. 1). Discussing results from different boxes is therefore the best strategy to investigate the evolution of this galaxy population. In order to ensure some mass resolution at higher redshifts, we have imposed an additional stellar mass cut: $M_{*}>10^{7}\,{\rm M_{\odot}}$ for TNG50 and TNG100, and $M_{*}>10^{8}\,{\rm M_{\odot}}$ for the lower resolution TNG300, across all snapshots.

We have opted to analyse only galaxies that are accreted at $z>1$ and maintain their identity as satellites all the way down to $z=0$. The motivation for this choice is twofold. First, it facilitates the analysis of the evolution of objects along the merger tree. Second, it allows us to probe a population of satellites that have been subject to mass stripping for a significant period of time. Note that our results are qualitatively consistent when the satellite redshift condition is shifted to $z=0.5$ and $z=2$. We have also checked that the redshift of last infall for these satellites is quite consistent between boxes: $1.57\pm 0.35$, $1.53\pm 0.34$, and $1.48\pm 0.33$ for TNG50, TNG100, and TNG300, respectively (where the variation ranges are simply obtained from the standard deviations). Here, the infall redshift is simply defined as the redshift at which galaxies become satellites for the last time (i.e., the last transition from central to satellite).

Fig. 4 compares the redshift evolution of the aforementioned population (second panel, from left to right) with that of $z=0$ satellites (i.e., imposing the “satellite" status only at $z=0$, first panel). The average infall redshift for this population in the boxes is $\sim 0.7$, with a standard deviation of $\sim 0.6$. The format displayed in Fig. 4 will be replicated in figures 5 - 9. The uncertainties on the measurements, represented by shaded regions, correspond to the standard errors on the mean (the object-to-object variation in these evolutionary trends for galaxies is known to be quite large). It is noteworthy that the results presented in Fig. 4 are qualitatively consistent with those from Chaves-Montero et al. (2016), using the EAGLE simulation (see their Fig. 12).

We begin by analysing the $z=0$-selected satellite population (leftmost panel of Fig. 4). The upper panel displays the average evolution of stellar and DM subhalo mass, along with the stellar-to-subhalo size ratio (i.e., the galaxy half-mass radius divided by subhalo half-mass radius, $R_{*}/R_{\rm sh}$), normalised to the corresponding value at $z=1$. Here, the TNG50, TNG100, and TNG300 results are represented by dashed, dotted, and solid lines, respectively. For statistical reasons, we have opted to employ the size measurements provided in the simulations, instead of those from Genel et al. (2018), but we have checked that our results do not depend strongly on this choice. Fig. 4 shows that, qualitatively, all boxes provide similar predictions. The average stellar mass grows from $z=1$ to $z=0$, whereas DM mass experiences a modest decrease due to tidal stripping (less than $50\%$ loss). As a consequence, the size ratio increases significantly, more rapidly than stellar mass. This picture is in agreement with previous findings that tidal stripping proceeds in an outside-in fashion: the stellar component, which is more concentrated and thus more tightly bounded to the potential well of the halo, is less affected by tidal effects (see, Engler et al. 2021; Smith et al. 2016).

The middle panel (of the leftmost plot in Fig. 4) shows the quenched fractions in the TNG boxes for the $z=0$ population. This is defined as the fraction of quiescent galaxies of the entire (corresponding) population (based on a redshift-independent sSFR threshold $\log_{10}(\rm{sSFR}[y^{-1}])<-10.5$, see, e.g., Lacerna et al. 2022). Results are again qualitatively consistent between boxes: a small fraction ($\lesssim 25\%$, depending on the box) of the population was already quenched at $z=1$. The quenched fraction increases towards $z=0$, reaching values between 60 and 75$\%$ (these results are in agreement with those from Donnari et al. 2021a; Donnari et al. 2021b using the IllustrisTNG simulation). Finally, in the lower panels of Fig. 4, the description is complemented with the baryon-to-DM mass fraction. The relative amount of gas decreases steadily as the population consumes their gas reservoirs, from $M_{\rm gas}/M_{\rm DM}\sim 0.1$ at $z=1$ to $M_{\rm gas}/M_{\rm DM}\sim 0.02-0.05$ at $z=0$. The stellar-to-DM mass ratio consequently increases (almost by an order of magnitude, from $M_{\rm*}/M_{\rm DM}\sim 0.02-0.04$ to $\sim 0.1$).

The fact that the TNG boxes map intrinsically different galaxy populations manifests itself in Fig. 4. The larger the TNG box, the larger the mean stellar and subhalo masses of satellites in halos of a given mass. This selection effect implies that satellites appear to grow stellar mass more rapidly in the larger boxes, whereas the DM mass drops less abruptly. The size/resolution of the TNG box has also a clear impact on the fraction of quiescent galaxies: the quenched fraction is $\sim$25 $\%$ lower in the TNG300 box as compared to the TNG50 box. Note that one could expect that lower resolution makes the mass stripping process more efficient (i.e., larger “chunks" of galaxies can be removed), but this is counteracted by the fact that TNG300 galaxies are more massive and (star-forming) active than TNG50 galaxies at fixed host halo mass. Interestingly, the evolution of the size ratio seems to be quite similar between boxes, independently of their distinct characteristics. In all boxes, $R_{*}/R_{\rm sh}$ increases by a factor of 3, resulting from the fact that the comoving stellar radius decreases less rapidly than the comoving subhalo radius.

On average, the $z=0$ satellite population has grown mass at a decent rate within the redshift range considered (increasing by a factor 2-3 from $z=1$). It is important to stress that this selection does not impose any constraint on the past identity of $z=0$ satellites (some of them are centrals at previous times). Results change significantly when we focus on a population that has suffered from mass stripping for a longer period of time (second panel of Fig. 4, fiducial subset). Note that this population corresponds to 18, 21, and 25$\%$ of the entire $z=0$ population in the TNG50, TNG100, and TNG300 boxes, respectively. In TNG300, the average stellar mass raises slightly (up to $\sim 20\%$ at $z\sim 0.5$), to then drop back to a value also slightly above the $z=1$ value at $z=0$. For TNG50/TNG100 populations, stellar mass actually decreases slightly within the redshift range considered. Note again that these average curves are the combined result of individual galaxies seeing their growth halted and even losing stellar mass at different times.

The little evolution of stellar mass is accompanied by a more dramatic DM reduction than in the previous sample (by as much as $\sim 75\%$), and a slightly steeper increase in the size ratio, whose evolution is now dominated by the shrinking of the DM component. The effect of mass stripping is also significant for the gas-to-DM mass fraction, which drops by an order of magnitude, i.e., from 10 to 1$\%$. The $M_{*}/M_{\rm DM}$ is higher at $z=1$ than before (for the $z=0$ sample). As compared to the $z=0$ population, the quenched fraction of $z>1$ satellites is significantly higher for all boxes, indicating that mass stripping accelerates the quenching mechanism (at $z=0$, all $z>1$ satellites are in a quiescent state). Note that there are of course two main concurrent mechanisms that affect this evolution: mass stripping and star formation. Part of the gas depletion is due to galaxies turning gas into stars.

The connection between mass stripping and quenching becomes more clear when the evolution of quiescent and star-forming galaxies is addressed separately (from left to right, third and fourth plots of Fig. 4, respectively). Here, we include satellites that remain quenched/star-forming during the entire redshift range (using the criteria explained above). Quenched galaxies lose stellar and DM mass steadily within the redshift range considered (up to $\sim 40$ and $\sim 70$ $\%$, respectively, at $z=0$). Note that we are subtracting the effect of mass growth due to star formation, so the effect of stellar mass stripping emerges clearly. Mass stripping in quenched galaxies produces variations in stellar mass, DM mass, and size ratios that are well represented by simple power laws of the form $\propto(1+z)^{\alpha}$. Finally, the lower panel shows that the stellar-to-DM mass ratio stays well above 0.1 throughout the redshift range considered for all boxes, increasing slightly due to the stronger DM stripping. As expected, the gas fraction is very low throughout.

Star-forming galaxies, conversely, display a less uniform evolution. The average stellar mass increases steadily up to a factor of 3-4 within the redshift range considered, but DM mass remains almost constant until $z=0.4$. After this redshift, the DM fraction drops significantly, which result in a sudden increase of the stellar-to-subhalo size ratio. Here, subhaloes lose on average $\sim$ 50 to 65$\%$ of their DM content, but mass stripping is insufficient to produce any change in the stellar mass growth of the population. The baryon-to-DM mass fraction is as expected: high (slightly increasing) gas fraction due to the loss of DM and a strong increase of the stellar-to-DM fraction due to star formation and DM loss.

Another interesting conclusion from Fig. 4 is that, almost independently of the box chosen and the satellite galaxy selection, the evolution of the size ratio is quite similar (an increase of a factor $\sim 3$ from $z=1$). In the following sections, we will dissect the effect of mass stripping in the $z>1$ satellite population. We will analyse the evolution of satellites as a function of both host halo mass and halo-centric distance. We will show that significant dependencies on the curves shown in Fig. 4 appear. Note that, statistically speaking, it is challenging to carry out this analysis controlling for stellar/subhalo mass (due to the mass ranges covered by the boxes). We have therefore opted to study the satellite population from TNG at “face value" (i.e. avoiding attempting to study the exact same stellar/subhalo mass ranges), but the reader must keep in mind that some of the differences discussed are due to the varying selection across boxes.

In order to study the effect of mass stripping in detail, we have determined the pericentric distance to the central galaxy ($d_{\rm peri}$) for each satellite in the fiducial sample. This is the minimum distance from the satellite to the corresponding central galaxy within the redshift range $0<z<1$ (it is, therefore, a single value within this interval). This and other similar measurements have proven more robust than the $z=0$ distance when it comes to evaluating the impact of the tidal field (e.g., satellites could be found far from the centre of the halo at $z=0$, despite having had a close encounter in the past). Four different subsets are defined based on normalised $d_{\rm peri}$ (pericentric distance divided by host halo virial radius): $d_{\rm peri}\leq 0.1$, $0.1<d_{\rm peri}\leq 0.4$, $0.4<d_{\rm peri}\leq 0.75$, and $d_{\rm peri}>0.75$. In this section, we begin by analysing low-mass haloes in TNG. Fig. 5 presents, in the same format of Fig. 4, the evolution of $z>1$ satellites in host haloes of masses $11\leq\log_{10}(M_{\rm host}[{\rm M_{\odot}}])<12$ for the four subsets described above. The subsets encompass in different boxes an average, from small to large $d_{\rm peri}$, of 13, 109, 46, and 24 objects, respectively. We also include the mean stellar mass of satellites in each subset. This is an important piece of information, since larger TNG boxes map typically more massive galaxies.

The effect of mass stripping is expected to become more noticeable as we move leftwards in Fig. 5. Independently of the simulation box selected, the DM content decreases more rapidly for smaller $d_{\rm peri}$. For $d_{\rm peri}>0.75$, the DM fraction is reduced by half in TNG50, whereas no significant evolution is observed in TNG300. For $d_{\rm peri}\leq 0.1$, conversely, DM is depleted to just a few percent of the $z=1$ mass content ($\sim$ 5$\%$ for TNG300 and $\lesssim$ 2$\%$ for TNG50). The progressive loss of DM for smaller distances results in a steeper evolution of the size ratio $R_{*}/R_{\rm sh}$.

Statistics are modest in Fig. 5, which explains the somewhat erratic behaviour of some of the curves shown. Although some differences exist, the growth in stellar mass appears fairly similar for different distances in all boxes. This evolution is very consistent with the quenched fractions. TNG300, which features the most massive satellites, displays the steeper stellar growth functions and, consequently, the lowest quenched fractions (barely any satellite is quenched at any redshift). The stellar mass growth flattens and the evolution of the quenched fraction steepens for progressively smaller TNG boxes. Fig. 5 therefore illustrates how differences between boxes at fixed halo mass and halo-centric distance can be attributed, at least partially, to systematically different galaxy/subhalo masses and quenched fractions. We will come back to this topic in Section 4.4.

The cyan arrows in the top panel of Fig. 5 indicate the average pericentric redshift, $z_{\rm peri}$ (i.e., the average redshift at which galaxies have their pericentric passage), for the TNG50 (solid) and the TNG300 boxes (open). The pericentric passage, as defined in this work, typically occurs at recent times in this mass bin ($z_{\rm peri}<0.2$ for $d_{\rm peri}<0.75$). The $z_{\rm peri}$ redshift increases with $d_{\rm peri}$, which is consistent with the fact that objects with large $d_{\rm peri}$ take more time to reach smaller distances. Fig. 5 also shows that larger boxes have larger $z_{\rm peri}$.

As mentioned before, Fig. 5 shows that DM tend to be stripped early on, which is consistent with the fact that it is stripped during the first close encounters (Smith et al., 2016). The magenta arrows indicate the average redshift at which the population reaches within a certain reference distance to the halo centre for the first time. This reference distance is set at 0.4$R_{\rm vir}$ in the first and second panels (from left to right) and 0.75$R_{\rm vir}$ in the third panel (no arrows are shown for the largest $d_{\rm peri}$). The magenta arrows indicate that satellites with the smallest $d_{\rm peri}$ also reach within close proximity to the central galaxy earlier on. The positions of the magenta arrows also roughly correlate with the redshifts at which DM starts to drop significantly, in agreement with the aforementioned results from Smith et al. (2016). A visual inspection of the evolution of the halo-centric distance for individual objects (for different $d_{\rm peri}$ bins) reveals that objects with small pericentric distances typically have short-period spiralling orbits from $z=1$ or above, whereas large values of $d_{\rm peri}$ usually correspond to long-period orbits where the satellite is still far from merging.

To summarise our results so far, we find no conclusive signs of significant baryonic mass stripping in Fig. 5, including gas and stellar mass. The evolution of these components seem to be dominated by star formation; only in TNG50, signs of an attenuated stellar mass growth start to be noticeable. Note that, even for $d_{\rm peri}\leq 0.1$, where DM is reduced by more than a factor 10, the effect on stellar mass is almost unnoticeable. Connecting this result with the SsHMRs of Fig. 3, it appears that the enhancement at the low-mass end could be at least partially driven by an excess of tidal stripping on the DM component of very small subhaloes (which has little effect on the stellar mass).

In Fig. 6, we look into slightly more massive haloes, i.e., $12\leq\log_{10}(M_{\rm host}[{\rm M_{\odot}}])<13$, where the number of objects are on average 284, 1362, 454, and 154, for increasingly higher $d_{\rm peri}$ bins (the average is computed for the 3 boxes). The effect of mass stripping on the baryonic content of satellites here becomes much more evident, as a clear trend with distance (relative to halo size) emerges. For $d_{\rm peri}<0.1$, stellar mass grows up to a redshift that ranges from 0.7 for TNG50 to 0.3 to TNG300, only to subsequently decrease down to $z=0$. As we move to larger $d_{\rm peri}$, the effect of mass stripping hindering the growth of stellar mass is progressively reduced. For $d_{\rm peri}>0.75$, stellar mass seems to grow almost unaffectedly for all boxes. Again, $R_{*}/R_{\rm sh}$ increases more rapidly for smaller halo-centric distances, remaining quite consistent between boxes. Interestingly, despite the different evolution in stellar mass, the DM mass loss is quite similar to that reported for smaller haloes.

An important result from Fig. 6 is the correlation between $d_{\rm peri}$, quenching, and stellar mass growth. For any given box, the closer the pericentric passage, the faster the satellite population quenches, and the more severe the mass growth attenuation. Interestingly, it is only when the quenched fraction reaches close to 100$\%$ that the average satellite ends up losing stellar mass (in a statistical sense). This (the stellar mass fraction being smaller than 1) only really happens for TNG50 and TNG100; in TNG300, the effect is not observed even when DM has dropped to less than 10$\%$ of its $z=1$ value. The effect of mass stripping is also noticeable from the lower panels of Fig. 6. The quenching manifestation of mass stripping is of course connected to the gas mass fraction, which typically drops more rapidly as the population gets closer to the centre of the halo. This trend seems to be discontinued in the closest-distance bin, potentially due to resolution effects.

The pericentric passage happens at slightly higher redshifts in Fig. 6, as compared to Fig. 5: $z_{\rm peri}\simeq 0.17$ for $d_{\rm peri}<0.1$ and $z_{\rm peri}\simeq 0.31$ for $d_{\rm peri}>0.75$ (on average for all boxes). The magenta arrows indicate that the first close encounter (defined through an arbitrary reference distance) happens at higher redshifts as well, as compared to Fig. 5. This could provide an explanation as to why the effect of stellar mass stripping is noticeable in the leftmost panel of Fig. 6, since satellites have been exposed to this mechanism for a longer period of time (as compared to satellites in Fig. 5). Also note that we are studying the effects in terms of distances normalised to halo size. Haloes in Fig. 5 are typically physically smaller.

Fig. 7 displays the evolution of satellite galaxies in host haloes of mass $13\leq\log_{10}(M_{\rm host}[{\rm M_{\odot}}])<14$, where the number of objects is on average 1379, 3544, 802, and 227, for increasingly higher $d_{\rm peri}$ bins. A good way to evaluate these results is to compare them with those for lower mass bins (Fig. 6). Starting from the $d_{\rm peri}\leq 0.1$ subset, we can see how the effect of mass stripping on the baryonic component of subhalos is more noticeable. For all boxes, the average stellar mass starts to decrease earlier and so does the gas-to-DM fraction. For host haloes of masses $12\leq\log_{10}(M_{\rm host}[{\rm M_{\odot}}])<13$, the gas fraction $M_{\rm gas}/M_{\rm DM}$ remains above $10^{-2}$, whereas for these more massive haloes it drops well below this threshold at $z=0$ ($M_{\rm gas}/M_{\rm DM}\simeq 3\times 10^{-3}-10^{-4}$, depending on the box). The quenching process is also significantly accelerated.

Although the effect of quenching and stellar mass stripping is more noticeable, the loss of DM is, interestingly, less pronounced. It is therefore incorrect to assume that a more significant DM loss will also imply a flatter stellar mass growth, in the average population sense. Galaxies that experience the closest encounters in these haloes retain more that $10\%$ of their DM mass. We have checked that the average $d_{\rm peri}$ within the $d_{\rm peri}\leq 0.1$ bin for these massive haloes is quite similar to that in less massive halos. Note, however, that distances are measured in virial radii, so a small $d_{\rm peri}$ for low mass haloes correspond to a smaller absolute distance. The fact that in smaller halos the orbits are more plunging (they reach closer to the central galaxy, in absolute terms) might explain the observed trends.

As a function of $d_{\rm peri}$, the trends that emerged in Fig. 6 remain in place, with the effect of mass stripping becoming less severe for higher distances: less quenching, higher gas fraction, more pronounced stellar mass growth, less DM loss. Importantly, the differences between boxes in each panel are significantly reduced as compared to lower halo mass bins, which implies that the effect of resolution and volume becomes less severe.

In Fig. 8, we look into the most massive haloes in the simulations: those in the halo mass range $14\leq\log_{10}(M_{\rm host}[{\rm M_{\odot}}])<15$ (1087, 2355, 425, 1012 objects on average between boxes in the $d_{\rm peri}$ subsets). Note that there are only a handful of subhaloes in the larger $d_{\rm peri}$ bins in TNG50, which explains the noisy results for this box. In order to avoid repetition, we will highlight two main conclusions from Fig. 8. First, the overall trends with $d_{\rm peri}$ are still in place. Second, at fixed $d_{\rm peri}$, the loss of stellar and gas mass becomes even more significant, and, consequently, so does the quenching, as compared to lower mass haloes. DM loss is quite similar, although slightly less pronounced, particularly for the lowest $d_{\rm peri}$.

Regarding the redshift of the pericentric and the first close encounters, the trends described in Section 4.2 still hold. At fixed $d_{\rm peri}$, satellites in more massive host haloes have their pericentric passage earlier on. In the most massive haloes (Fig. 8), we find, on average: $z_{\rm peri}\simeq 0.27$ for $d_{\rm peri}\leq 0.1$ and $z_{\rm peri}\simeq 0.42$ for $d_{\rm peri}>0.75$. On the other hand, satellites with $d_{\rm peri}\leq 0.1$ in massive haloes were within 0.4$R_{\rm vir}$ already at $z\gtrsim 1$.

Finally, we have checked that, qualitatively, the main results of the paper remain valid when the $z=0$ halo-centric distance, instead of the pericentric distance, is employed. Interestingly, binning by $z=0$ distance produces slightly larger mass losses than binning by $d_{\rm peri}$ (both in stellar mass and DM mass). The reason behind this general agreement is that, as shown above, satellites tend to have spiralling orbits, so those objects with the smallest $d_{\rm peri}$ tend to reach proximity at recent times (also we have only analysed objects that remain satellites at $0<z<1$).

Figs. 5 - 8 show that, qualitatively, the TNG boxes provide similar predictions for the average evolution of satellites, even when these are split by host halo mass and pericentric distance. Quantitatively, however, differences are apparent across the array of measurements performed in this analysis, due to the fact that boxes map different stellar mass (and subhalo mass) ranges. In this section we explicitly show this point: most of the differences found are the result of each box mapping intrinsically different populations in terms of stellar mass and/or subhalo DM mass.

In Fig. 9, we pick two different bins in host halo mass vs. distance space: $12\leq\log_{10}(M_{\rm host}[{\rm M_{\odot}}])<13$, with $d_{\rm peri}\leq 0.1$ (Fig. 6) and $13\leq\log_{10}(M_{\rm host}[{\rm M_{\odot}}])<14$, with $0.1<d_{\rm peri}\leq 0.4$ (Fig. 7). In both cases, we impose narrow $z=0$ stellar mass ranges of $9.2<\log_{10}(M_{\rm*}[{\rm M_{\odot}}])<9.5$ and $9<\log_{10}(M_{\rm*}[{\rm M_{\odot}}])<9.1$, respectively. This allows us to (approximately) fix the mean $z=0$ stellar mass in the three boxes, of course at the expense of losing statistics. Despite this caveat, Fig. 9 shows that the differences observed in almost all properties are reduced considerably (particularly, as expected, for stellar mass growth and quenched fraction). In most cases, these differences are fairly consistent with the statistical error on the mean.

Note that there is of course very large intrinsic stochasticity in the evolution of galaxies, which is reflected in these properties. As an example, the standard deviations (object-to-object) in the $z=0$ stellar growth ratios are $\sim$0.46, 0.8, and 1.8 for the TNG50, TNG100, and TNG300 boxes, whereas the standard deviations for the $z=0$ DM fractions are $\sim$0.03, 0.1, and 0.06, respectively (even after controlling for stellar mass). The differences that still remain could also be due to the scatter in the SsHMR.

Characterising the effect of varying resolution on the evolution of satellite galaxies as predicted by the TNG boxes is outside the scope of this paper, as it would require a more in depth analysis at the particle level. However, Fig. 9 shows that differences between boxes are relatively small (given the intrinsic variation in the data) when the analysis is performed at fixed stellar mass. This allows us to use the boxes to evaluate the stellar mass dependence. Our results also suggest that the quenching would not depend strongly on resolution.

The effect of mass stripping is significantly stronger, as Figs. 5 to 8 demonstrate, for the DM component of subhaloes than it is for stellar mass. This is expected, not only because the DM component is much more extended and less concentrated, but also because galaxies inside subhaloes continue forming stars (thus turning gas into stars). In this section, we evaluate the extreme case where subhaloes reach a point of DM loss where stellar mass becomes the dominant component. This analysis is connected with recent observational claims of the existence of galaxies containing no (or very little) DM (see van Dokkum et al. 2018; van Dokkum et al. 2019).

The $z=0$ population of DM-deficient satellites is highlighted in the $M_{*}/M_{\rm DM}$ vs. $M_{\rm DM}$ plot of Fig. 10, as those objects lying above the horizontal dashed line. These galaxies are defined by the condition that the stellar-to-DM ratio is greater than 1. There are several important conclusions to extract from this figure. First, DM-deficient satellite galaxies are found in all TNG boxes. They correspond less than 1$\%$ of the TNG50, TNG100, and TNG300 galaxy populations at $z=0$. Second, they span a relatively wide range of subhalo DM masses, i.e., they are not only found in low-mass subhaloes, where resolution effects might be a concern. They, however, tend to avoid the most massive subhaloes, as expected from tidal stripping. Third, the most extreme cases, where the stellar-to-DM ratio reaches a factor as high as 10 tend to correspond to the smallest subhaloes. Finally, DM-deficient satellite galaxies also tend to reside in massive host haloes ($M_{\rm host}\gtrsim 10^{13}$ M_⊙).

The latter aspect is addressed in more detail in Fig. 11, where the probability density distribution of mass for haloes hosting the DM-deficient population at $z=0$ is displayed for the TNG boxes. We also show here the distribution of host haloes for the progenitors of the $z=0$ population, at redshifts $z=1$ and $z=2$. Fig. 11 shows that DM-poor galaxies tend to favour massive haloes even at $z=1$. Note that massive host haloes are less common, but they also contain more satellites. Another related question of interest is the location of these galaxies within their host haloes. We have estimated that the average halo-centric distance for DM-poor satellites at $z=0$ is $\sim$0.36, 0.44, and 0.34 virial radii in the TNG50, TNG100, and TNG300 boxes, respectively. However, most of these objects have experienced very close encounters in the past, as confirmed by their pericentric distances: $d_{\rm peri}\simeq$ 0.05, 0.05, and 0.03 $R_{200}$, respectively. They belong, therefore, to the closest distance bin defined in Figs. 5 to 8.

We have also checked that all DM-deficient galaxies are indeed satellites at $z=0$ in the three TNG boxes. In fact, there are only a handful of instances along the merger trees of the three boxes where a central galaxy is DM-poor. In Fig. 12, the fraction of these systems of the total satellite population at each snapshot is displayed for the three boxes as a function of redshift. For all boxes, the fraction increases from $z=2$, reaching a discrete $\sim$1-2$\%$ at $z=0$. This evolution with redshift is totally consistent with the idea that these systems lose their DM through close encounters. These encounters are expected to be progressively more likely given the hierarchical nature of structure formation.

Among central galaxies at $z=0$, the most DM deficient objects have $M_{*}/M_{\rm DM}$ ratios of 0.3-0.4. These objects are also special when it comes to their recent evolution. While more than 70$\%$ of centrals were already centrals at $z=2$, those objects for which $M_{*}/M_{\rm DM}>0.1$ only became centrals (for the last time) at (median and standard deviation) $z=0.11\pm 0.17,0.15\pm 0.15$, and $0.08\pm 0.06$ in the TNG50, TNG100, and TNG300 boxes, respectively. Again, the fact that they were recently satellites is consistent with the notion that DM deficiency is connected with tidal stripping. These objects can be associated with splashback galaxies (i.e., central galaxies at $z=0$ that live in the vicinity of massive haloes and were satellites in recent times).

In Table 1, we list average values (and standard deviations) for some of the main properties of DM-deficient satellites in TNG. One interesting aspect to highlight is that the smaller TNG boxes (which have higher resolution) predict higher average stellar-to-DM mass fractions, reaching a factor of 2 for TNG50/TNG100 (this might be, however, affected by statistics, since these boxes have significantly fewer objects above the threshold). The size ratio, on the other hand, is $R_{*}/R_{\rm sh}\sim 1$ in all boxes, showing how tidal stripping and interactions with the central galaxy has bared these subhaloes to the very core. The great majority of these galaxies are, as expected, quenched ($\sim 90\%$). Finally, most of them have very high infall redshifts, around $z_{\rm infall}=1.4$ (note that this is a lower limit, since we have only employed merger trees up to $z=2$). In fact, around $70\%$ of DM-poor satellites at $z=0$ in each box pertain to our fiducial subset of galaxies that were accreted at $z>1$ and remain satellites ever since.

These results allow us to explain the presence of baryon-dominated galaxies as a result of the loss of material that happens in galaxy groups or clusters, without the need to invoke any mechanism that could potentially contradict the hierarchical merging scenario for galaxy formation. DM-deficient galaxies, such as the ones allegedly observed in van Dokkum et al. (2018); van Dokkum et al. (2019), seem to have a pretty standard origin, representing simply the extreme tail of the tidally stripped satellite galaxy population.

It is important to stress that this analysis could be potentially affected from a quantitative standpoint by identification issues from the subfind algorithm (Muldrew et al., 2011; Springel et al., 2021), which uses only 3D and not velocity information.