University of Groningen
Bachelor Thesis in Astronomy
Characterization of a simulated minor merger resembling Gaia-Enceladus
Author: Supervisors: prof. dr. Amina Roy O. Y. Bos Helmi Helmer H. Koppelman
Abstract The second Gaia data release (Gaia Collaboration et al., 2018a) has provided evidence for a merger event roughly 10 Gyr ago with an object named Gaia-Enceladus (Helmi et al., 2018). A previous simulation by Villalobos and Helmi (2008, 2009) produced a similar velocity distribution of halo stars near the Sun as seen in the Gaia data. In this bachelor thesis I continue this simulation for 10 Gyr in an attempt to characterize stars of Gaia-Enceladus, which accounts for a large fraction of the galactic halo and possibly triggered the formation of the thick disk. The aim of the thesis is to help interpret the observations and to provide means to ﬁnd likely members of Gaia-Enceladus in the Gaia data, especially at large distances from the Sun. I ﬁnd that the characteristic kinematics of the accreted stars are maintained through the extension of the simulation and still show similarities to the various features seen in the Gaia data. These features can be understood well when analyzing the angular momentum and eccentricity as they are correlated to the initial position of the stars, and to the mass loss history.
July 2019 CONTENTS CONTENTS
1 Introduction 1 1.1 Milky Way components ...... 1 1.2 Gaia mission ...... 1 1.3 Gaia-Enceladus ...... 1 1.4 Thick disk and halo formation ...... 2 1.5 Velocity ...... 2 1.6 Thesis description ...... 3
2 Simulations 4 2.1 Description ...... 4 2.2 Dark matter halo ...... 4 2.3 Host galaxy ...... 5 2.4 Satellite galaxy ...... 6 2.5 Numerical parameters ...... 6 2.6 Change of coordinate system ...... 7
3 Results 8 3.1 Morphology ...... 8 3.2 Velocity ...... 11 3.3 Angular momentum ...... 13 3.4 Eccentricity ...... 14 3.5 Eccentricity and angular momentum ...... 17 3.6 Metallicity ...... 20
4 Discussion 21
5 Summary and conclusion 22 1 Introduction
1.1 Milky Way components
The Milky way consists of several distinct components, each having diﬀerent properties. Figure 1 schematically shows each component in a side-on view of the Milky Way (Buser, 2000). The galactic center contains a supermassive black hole and mostly young giant stars. The galactic center is embedded in the galactic bulge. This is a nearly spherical collection of mainly old stars. Most stars in the Milky Way are located in the disk, which has a diameter of up to 60 kpc (L´opez- Corredoira et al., 2018). This disk can be subdivided into a thin disk and a thick disk, which show clear diﬀerences in origin. The thin disk contains a lot of gas and thus has, on average, younger stars compared to the thick disk. Lastly, the galactic halo surrounds the Milky Way and is extended in all directions. The galactic halo mainly contains old stars. The Milky Way is also thought to have a halo of dark matter extending much farther out.
Figure 1: A diagram showing the diﬀerent components of the Milky Way.
1.2 Gaia mission
In late 2013, the European Space Agency launched the Gaia satellite. Its mission is to measure the three-dimensional positions and velocities of stars in the Milky Way and to determine their intrinsic properties (Gaia Collaboration et al., 2016). The second Gaia data release (DR2) contains the positions and apparent brightness of 1.7 billion stars (Gaia Collaboration et al., 2018a). More importantly for this thesis, the data release also includes the proper motions of 1.3 billion stars and line-of-sight velocities for 7 million stars. Alongside the kinematical information of these stars, the Gaia data release also measured colours for 1.3 billion stars and derived the intrinsic properties such as temperature, stellar radius and luminosity for a subset of these stars. However, the data release does not include the metallicity and abundances in the stars. For this it is necessary to combine the Gaia data set with other data sets such as APOGEE, RAVE and LAMOST.
DR2 also revealed that the Herzsprung-Russell diagram of stars in the stellar halo has two se- quences (Gaia Collaboration et al., 2018b); a red, metal rich sequence and a blue, metal poor sequence. This hints that the halo consists of two stellar populations of diﬀerent origin. Koppel- man et al. (2018) has shown using kinematic data from DR2, that some of the stars in the solar
1 1.4 Thick disk and halo formation 1 INTRODUCTION neighbourhood are part of a large retrograde moving kinematic structure. The stars in this retro- grade structure trace the metal poor (blue) sequence found in Gaia Collaboration et al. (2018b). Helmi et al. (2018) proposed that the stars from this retrograde component are debris from an ob- ject that merged with the Milky Way about 10 Gyr ago, to which they refer to as Gaia-Enceladus. They state that the debris from Gaia-Enceladus dominates the inner halo. Furthermore, using isochrones they show that the members of Gaia-Enceladus span a range of ages of 10 - 13 Gyr. The results of Koppelman et al. (2018) agree well with Vincenzo et al. (2019) and Gallart et al. (2019), which put the median age of Gaia-Enceladus at 12.33 Gyr and 12.37 Gyr, respectively
1.4 Thick disk and halo formation
If Gaia-Enceladus had indeed merged with a disk-like galaxy, it must have caused this disk to dynamically heat. Dynamical heating entails that gravitational interactions with stars of Gaia- Enceladus cause the stars from the disk to have a larger spread in velocity. This would thus result in a thicker disk. Hence, Gaia-Enceladus has been proposed to be at least partly responsible for the formation of the thick disk in the Milky Way (Helmi et al., 2018). We can even expect that some stars from the pre-existing disk were dynamically heated towards the halo. This is supported by Purcell et al. (2010) and Pillepich et al. (2015), which both use simulations to show that a considerable part of the pre-existing thick disk stars end up in the halo. Furthermore, Haywood et al. (2018) ﬁnds using observational data that the red, metal rich sequence could be the low rotational velocity tail of the old galactic disk. This further supports the hypothesis that Gaia-Enceladus caused the precursor of the thick disk to dynamically heat, causing some disk stars to end up in the halo. The newly accreted gas could also have lead to a burst of star formation. As Gallart et al. (2019) shows, the thick disk reached its peak in star formation about 9 Gyr ago, 4.5 Gyr after the formation of the ﬁrst stars in the Milky Way. After a few gigayears, the gas would settle into the thin disk, where star formation still continues to this day (Vincenzo et al., 2019).
The kinematic properties of stars allow us to make distinctions between diﬀerent populations of stars. For instance, the angular momentum of a star could be conserved over time, depending on the properties of the gravitational potential. The angular momentum of a star that we can currently measure could thus be related to the angular momentum it had during the time of the merger event. Since it is quite a plausible assumption that the stars from Gaia-Enceladus had, on average, diﬀerent angular momenta, we could expect to see two distinct angular momentum distributions in the Gaia data. The velocities that stars in the solar neighbourhood have are related to their energy and angular momentum. Stars with negative angular momentum, for example, have negative vφ. Hence, if there is a net diﬀerence in the angular momentum of the stars from the disk and from Gaia- Enceladus, there should be a diﬀerence in vφ. Figure 2 (Helmi et al., 2018) shows the stellar velocity distribution in the solar vicinity retrieved from the second Gaia release (Gaia Collaboration et al., 2018a) and from a 5:1 mass ratio merger simulation performed by Villalobos and Helmi (2008, 2009). The ﬁgure shows that a large fraction of halo stars within the solar neighbourhood is part of a kinematic structure with a slightly retrograde motion (Vy < 0). The simulation, shown at 4 Gyr from the start of the simulation, shows similarities with the velocity distribution from the observations. The simulation shows that the stars from the satellite galaxy (shown in blue) consist of a main component with slightly retrograde movement and a highly retrograde component at Vy < −300 km/s, which is consistent with the ﬁndings based on Gaia DR2.
2 1.6 Thesis description 1 INTRODUCTION
Figure 2: Velocity distribution of the stars in the solar vicinity (Helmi et al., 2018). The left panel shows the velocity diagram retrieved from the Gaia data. The blue stars indicate likely members of Gaia-Enceladus, selected by angular momentum and energy. The right panel shows the velocity distribution retrieved from the merger simulation of Villalobos and Helmi (2008, 2009) at t = 4 Gyr. Host stars are shown in black and satellite stars are shown in blue. The simulation was carried out on a smaller scale so the velocity diagram was scaled up by a factor 1.5 to resemble the Gaia data.
1.6 Thesis description
In this thesis I carry out four N-body simulations, which model a minor galactic merger with a mass ratio of 5:1. The simulations continue from the simulations carried out by Villalobos and Helmi (2008, 2009). As pointed out by Helmi et al. (2018), one of these simulations shows similarities in velocity space with the data from DR2 (Gaia Collaboration et al., 2018a). In this thesis I assume that the satellite galaxy that merges with the disky host galaxy in this simulation is representative of Gaia-Enceladus. The aim of this thesis is then to use this simulation to characterize the members of Gaia-Enceladus. The simulations are carried out over a period of 10 Gyr, which is the estimated time since the merger happened (Helmi et al., 2018). The properties of the simulation are discussed in detail in Section 2. Each simulation contains 800 000 particles which are distributed in a satellite galaxy and a disky host galaxy. Both galaxies consist of a stellar component and a dark matter component. Each component has 100 000 particles except for the dark matter in the host galaxy, which has 500 000 particles. Gas physics and star formation are not included. All stars are thus present from the start of the simulation. The simulations consist of several cases. The case that is explored in most detail this thesis is that of a retrograde moving disky satellite which is launched at an inclination of 30 degrees with respect to the host disk. Three other simulations were executed, each varying one aspect of the aforementioned case; one with a prograde moving satellite, one with a spherical satellite and one which launches the satellite at an inclination of 60 degrees. I proceed to analyze to simulations. Section 3.1, I show how the spatial distribution of stars in the host and satellite galaxy change over time. In Section 3.2, I describe the kinematics of the stars. In the next two sections, Sections 3.3 and 3.4, I present the angular momentum and eccentricity distributions. These properties are then correlated to the positions of the stars at the ﬁrst available snapshot in Section 3.5. Subsequently these results are interpreted in the context of abundance gradients in Section 3.6.
3 2 Simulations
The simulations were carried out using the Gadget-2 cosmological simulation code Springel (2005). As input for each simulation, I used data of the last snapshot of the simulations carried out by A. Vill´alobos Villalobos and Helmi (2008), resuming the simulations at t = 1 Gyr. Unfor- tunately though, the data from the ﬁrst part of the simulations could not be found. Hence I could not fully analyze the initial situation. It was previously found in Helmi et al. (2018) that the results of the simulations favour a retrograde merger with a disky satellite galaxy at an inclination of 30 to 60 degrees. Unless mentioned otherwise, the results in this paper refer to the 30 degrees case. Three other simulations were carried out for comparison, each changing one parameter. The ﬁrst simulation has an inclination of 60 degrees instead of 30, the second simulation features a prograde moving satellite instead of a retrograde one and the last simulation models a spherical satellite instead of a disky satellite. Both the host and the satellite galaxy are conﬁgured such that they resemble a system at redshift z = 1, following the model of Mo et al. (1998). This results in a combined stellar mass of the host and satellite galaxy that is roughly equal to the mass of the present day thick disk. At the start of the simulation by Villalobos and Helmi (2008), the satellite galaxy is released from a distance of 83.9 kpc which corresponds to the virial radius of the host galaxy at z = 1.6. The initial positions, velocities and angular momenta of the satellite galaxy are shown in Table 1 (Villalobos and Helmi, 2008).
i x y z vx vy vz Lz 30° 72.7 0 42.0 -102.4 -91.8 -59.1 -5729.5 60° 42.0 0 72.7 -59.1 -91.8 -102.4 -3307.9
Table 1: Initial positions, velocities and angular momenta of the satellite galaxy for both inclinations. Positions are in kpc, velocities in km s−1 and angular momenta in kpc km s−1. In the case of the prograde simulation, vy and Lz change sign.
Villalobos and Helmi (2009) uses scale lengths that are 35% smaller than that of the Milky Way. Thus, in some cases, the system is scaled by a factor 1.5 so that it resembles the Milky Way.
2.2 Dark matter halo
Both galaxies contain a halo of dark matter particles. These follow an NFW mass density proﬁle Navarro et al. (1997), which is given by
ρs ρNFW(r) = 2 , (1) (r/rs)(r + r/rs) where ρs is the characteristic scale density and rs is a scale radius. This density is consistent with cosmological simulations and has a well known dependence on redshift, described in Wechsler et al. (2001). The scale radius rs is given by R r = vir , (2) s c
4 2.3 Host galaxy 2 SIMULATIONS
where Rvir is the virial radius and c is the concentration parameter. The concentration parameter is given by:
−0.13 20 Mvir(z) c ≈ 11 . (3) 1 + z 10 M
Here, Mvir is the virial mass. Both the virial masses and virial radii at z = 0 are given in Table 2 and Table 3. A derivation of the virial mass is given in Villalobos and Helmi (2008). The virial mass depends on redshift as:
−2acz Mvir(z) = Mvir(z = 0)e , (4) with ac a constant deﬁned as the formation epoch of the halo, assumed to be ac = 0.34. This simulation further assumes a ﬂat cosmology with a baryon density of Ωm(z = 0) = 0.3, a vacuum −1 −1 energy density of ΩΛ = 0.7 and a Hubble parameter of H(z = 0) = 70 km s Mpc .
2.3 Host galaxy
Villalobos and Helmi (2008) model the host galaxy as a self-consistent system. Thus, if the host galaxy is evolved in isolation, its properties are relatively stable for the entire duration of the simulation. However, it must be mentioned that Villalobos and Helmi (2008) observe the formation of a bar after 7 Gyr, meaning that the host galaxy is no longer in equilibrium. Since the merger occurs before this timescale, this is not an issue for the simulations presented here. The density proﬁle of the stellar disk, as outlined in Hernquist (1993) and Quinn et al. (1993), is given as Md R 2 Z ρd(R, Z) = 2 exp − sech , (5) 8πRDZ0 RD 2Z0 where Md is the disk mass, RD is the exponential scale length and Z0 is the exponential scale height. The computational parameters of the host galaxy are given in Table 2.
NFW halo 11 Virial mass, Mvir 5.07 × 10 (M ) Virial radius, Rvir 122.22 (kpc) Concentration, c 6.56 −1 Circular velocity, Vc(Rvir) 133.87 (km s ) Number of particles, NH 500 000 Softening, halo 0.42 (kpc)
Disk 10 Disk mass, Mdisk 1.2 × 10 (M ) Scale length, RD 1.65 (kpc) Scale height, Z0 0.165 (kpc) Toomre Q(R = 2.4RD) 2.0 Number of particles, ND 100 000 Softening, disk 0.012 (kpc)
Table 2: Parameters of host galaxy. The softenings are discussed in Section 2.5.
5 2.4 Satellite galaxy 2 SIMULATIONS
2.4 Satellite galaxy
Just like the host, the satellite galaxy is also modeled as a self-consistent two-component system with an NFW dark matter halo. The stellar distribution of the satellite is modeled for the case of an exponential disk proﬁle and a Hernquist bulge proﬁle (Hernquist, 1990), given as:
Mb ab ρb = 3 . (6) 2π r(r + ab)
The parameters of the satellite galaxy are given in Table 3. It includes the two cases of a disky and spherical satellite.
NFW halo 11 Virial mass, Mvir 1.01 × 10 (M ) Virial radius, Rvir 71.35 (kpc) Concentration, c 8.09 −1 Circular velocity, Vc(Rvir) 78.10 (km s ) Number of particles, NH 100 000 (kpc) Softening, halo 0.07/0.14 (kpc)
Disk 9 Disk mass, Mdisk 2.4 × 10 (M ) Scale length, RD 0.96 (kpc) Scale height, Z0 0.095 (kpc) Toomre Q(R = 2.4RD) 2.0 Number of particles, ND 100 000 Softening, disk 0.007 (kpc)
Bulge 9 Bulge mass, Mbulge 2.4 × 10 (M ) Scale radius, ab 0.709 (kpc) −1 Velocity dispersion, σ0 69.06 (km s ) Number of particles, NB 100 000 Softening, bulge 0.07 (kpc)
Table 3: Parameters of satellite galaxy. The softenings halo are for a disky and spherical satellite respec- tively. The softenings are discussed in Section 2.5.
2.5 Numerical parameters
The gravitational force softening modiﬁes the gravitational potential of particles at small scales to prevent numerical divergences (Springel, 2005). If this parameter is set too small, particles may either clump together or ﬂy oﬀ during close encounters. Meanwhile, a force softening that is too high will lead to inaccurate results. This parameter also inﬂuences the time step of the simulation. The time step that is used for one particle in the simulation is given by the relation
∆t =p2η/|a|, (7) where η = 0.025 deﬁnes the error tolerance and a is the acceleration of the particle. The maximum time step was set to 0.25 Myr.
6 2.6 Change of coordinate system 2 SIMULATIONS
2.6 Change of coordinate system
The coordinate system that is used in the simulation is not particularly useful as it is not centered on the host galaxy. To better examine the data, I apply a change of the coordinate system. First, the positions are recentered such that the origin coincides with the center of mass of the stellar host particles. Then the velocities are shifted such that the total momentum of the disk particles is zero. This ensures that the host disk is at rest in our frame of reference. At this point, the system is centered on the host galaxy. However, there is no meaningful distinc- tion between the ˆx, ˆy and ˆz-directions as the disk is not aligned to any of the coordinate planes. In many cases it is thus useful to align the xy-plane with the plane of the disk. To do so, the total angular momentum of the stellar host particles was set to align with the z-axis of the coordinate system. This was done by applying two rotations. The positions of the particles were multiplied with the rotation matrices cos θxy − sin θxy 0 Rz(θ) =sin θxy cos θxy 0, (8a) 0 0 1 cos θxz 0 sin θxz Ry(θ) = 0 1 0 (8b) − sin θxz 0 cos θxz where θxz and θxy are the angles between the angular momentum of the host galaxy L~ host and the xz and xy plane respectively. Lastly, to construct the velocity diagrams it is useful to convert to cylindrical coordinates for the velocities. An easy way to do this is to ﬁnd the rotation matrix necessary to change the position of one particle such that it coincides with the x-axis. This matrix is given by Equation (8a), where θxy is the angle between the position of the particle and the xy-plane. Applying the rotation matrix to the velocity vector results in a cylindrical velocity.
Figure 3: Schematic of the rotation used to ﬁnd the velocities in cylindrical coordinates. The left diagram shows the situation before the rotation matrix has been applied. The velocities after the rotation, 0 0 vx and vy, correspond to vR and vφ respectively in the left diagram.
7 3 Results
To generate the results, I use the cosmological simulation code Gadget-2 by Springel (2005). By default, the Gadget-2 simulation gives a binary output. To convert this to a usable format, I used the package pyGadgetReader (Thompson, 2014). Subsequently, the data was processed using the Python code language.
The positions of the satellite and host stars are shown in Figures 4 and 5 respectively. Each panel is shown in a reference frame that is aligned with the host disk at t = 0 Gyr. Note that the satellite is shown on a larger scale. The stars from the satellite are more extended and rounded in morphology compared to those from the host galaxy, which maintains a relatively disky form. Over time, the stars from the satellite galaxy slowly start to align with the host galaxy.
Figure 4: Evolution of the satellite galaxy over time. In each panel the system uses the coordinate system at t = 0. Hence the xy-plane is aligned with the plane of rotation of the host disk just before the merger.
8 3.1 Morphology 3 RESULTS
Figure 5: Evolution of the host galaxy over time. Again, all panels use the coordinate system that is aligned with the host disk just before the merger.
Between 1 and roughly 3 Gyr from the start of the simulation, several shells are visible. Though faint, shells are also observed in some real galaxies. These shells emerge when a collections of stars have similar apocenters. Shells can thus be distinguished by an increased stellar density at a particular galactocentric distance, as can be seen in Figure 6. This shows the radial density distribution at t = 1.44 Gyr and shows clear peaks in the density.
Figure 6: Radial density distribution of the satellite particles at t = 1.44 Gyr. Figure 7 shows the positions of particles in the outer shell at 34 < r < 37 kpc.
Figure 7 shows the evolution of a selection of stars from a shell at t = 1.44 Gyr, in the system that is aligned with the host disk at each time. Stars from these shells have similar kinematics and thus a similar apocenter and pericenter. When these stars are near their pericenter, they form streams
9 3.1 Morphology 3 RESULTS
passing through the central region of the galaxy. At t = 5 Gyr, the streams passing through the center are still clearly visible on some occasions, such as at t = 5.14 Gyr. The streams are visible for at least 6 Gyr. After 8 Gyr, stars from a common shell are almost uniformly distributed up until the initial outer radius of the shell.
Figure 7: Evolution of the positions of stars from a shell. The shell stars are shown in red while the stars from the satellite galaxy are shown in black. The shell stars are selected at t = 1.44 Gyr to have galactocentric distances of 34 < r < 37 kpc. In each panel, the system is aligned with the host disk at that particular time.
10 3.2 Velocity 3 RESULTS
Figure 8 shows the velocity distribution of stars in the solar vicinity after a time of 10 Gyr, in the reference frame that is aligned with the host disk at that time. Because the simulation assumes a scale length that is 35% smaller than that of the Milky Way, the velocities have been multiplied by a factor 1.5 to resemble what we would expect from the Milky Way. The right panel in Figure 8 shows the vR - vφ velocity space. It can be seen that the stars from the satellite form arches on the side. All the stars within the volume have a diﬀerent orbital phase. For instance, stars with vR = 0 are at their apocenter or pericenter.
Figure 8: Velocity distribution of stars in the solar vicinity after 10 Gyr. Stars from the satellite are shown in orange while those from the host are shown in blue. In both panels, the system is aligned with the host disk at that time. Similar to Figure 2b, the positions and velocities were scaled with a factor 1.5 to resemble the Gaia data. The stars were selected to be within a sphere of radius r = 1.5 · 2.5 kpc at a distance of RS = 1.5 · 2.4RD from the origin. Here, RD is the scale length deﬁned in the simulation. See Table 2 for the values of RD.
The velocity distribution looks very similar to that at t = 4 Gyr, shown in the right panel of Figure 2. The time evolution of the velocity diagram is shown in Figure 9. The arch shaped feature that appears in the left panel of Figure 8 at vφ < −300 km/s varies a bit with time. It is present through most of the simulation time after t = 1 Gyr, but the sharpness of this arch feature depends on the exact time. Overall there seems to be little to no evolution of the velocity diagram as a whole.
11 3.2 Velocity 3 RESULTS
Figure 9: This ﬁgure shows the evolution of the velocity diagram over time. At each panel, the system is aligned with the host disk at that time. Again, to resemble the properties of the Milky Way, the velocities and positions are scaled with a factor 1.5. The stars were selected to be within a sphere of radius r = 1.5 · 2.5 kpc at a distance of 1.5 · 2.4RD from the origin. Here, RD is the scale length of the host galaxy deﬁned in the simulation, and is given in Table 2.
Figure 10 shows the same velocity diagram at t = 10 Gyr but at diﬀerent positions. At larger distances from the center of the galaxy, there is a more clear distinction between the host stars and the satellite stars. At large distances, the stars from the satellite galaxy have more radial orbits (vφ ≈ 0), while the host stars have more circular prograde orbits. This results in a separation in vφ.
Figure 10: Velocity diagram as a function of the position of the selection. Again, the system is scaled with a factor 1.5. The factors in the top left indicate the galactocentric distance of the selection in units of RS = 1.5 · 2.4RD. The radius of the selection is 1.5 · 2.5 kpc.
12 3.3 Angular momentum 3 RESULTS
3.3 Angular momentum
Figure 11 shows the angular momentum distribution as a function of cylindrical radius from the center of mass of the host. The diﬀerent panels show the distribution at t = 2 Gyr and t = 10 Gyr respectively. In both cases a coordinate system is used that is aligned with the host disk at that time. However, the system is not scaled with a factor 1.5. As the angular momentum is given by L = r × p, scaling the positions and velocities would result in a factor 1.52 = 2.25 increase in angular momentum. The ﬁgure shows that the host stars are clearly separated from the satellite stars, especially at high radial distances. Although the distribution does lose substructure, the separation between the two populations is stable over time.
Figure 11: Angular momentum distribution as a function of cylindrical radius. The angular momentum is given in the reference frame aligned with the host disk at t = 2 Gyr and t = 10 Gyr, respectively. The stars are selected to be within 2 < R < 12 kpc and |z| < 1 kpc such that only the stars in the plane of the disk are selected. Stars from the satellite are shown in orange while those from the host are shown in blue.
Figure 12 shows histograms of the angular momentum, again at 2 Gyr and at 10 Gyr. The host and satellite particles have an equal number of particles in the simulation and therefore the histograms have been scaled to reﬂect their relative masses. It can be seen that over time, the distribution of the satellite gets wider while the distribution of the host gets narrower. For the ﬁrst few Gyr there is some unevenness in the distributions but after roughly 8 Gyr these are mostly smoothed out.
13 3.4 Eccentricity 3 RESULTS
Figure 12: Stacked histogram of the angular momentum in the ˆz-direction, in the reference frame aligned with the host disk. The histograms are weighted by mass. Again, the left panel is at t = 2 Gyr, and the right panel at t = 10 Gyr. Stars from the satellite are shown in orange while those from the host are shown in blue.
The eccentricity of an orbit is given as r − r = max min , (9) rmax + rmin
where rmax is the apocenter of the orbit and rmin is the pericenter of the orbit. To accurately calculate the eccentricity of a particle, it is necessary to follow the particle’s position for several orbital periods. One method of ﬁnding the eccentricity involves taking the positions and velocities of each particle at a particular time and integrating their orbits separately in an external potential. This, however, may not be representative of the actual gravitational potential of the simulation as the outcome depends on the choice of the gravitational potential. For simplicity, I have opted to use the positions directly from the simulation. Although this method reﬂects more the physics of the actual system, it also comes with drawbacks. For instance, it is not possible to get the instantaneous eccentricity of a particle. The radial distance of each particle was calculated at each time step between 7.5 < t < 10 Gyr. Each local maximum and minimum in the orbital radius represents the apocenter and pericenter of an orbital revolution. To estimate each particle’s eccentricity, I took the mean of all the apocenters and pericenters. This eccentricity can thus be considered to be the average eccentricity between 7.5 < t < 10 Gyr. Figure 13 shows the eccentricity distributions for all four simulations. The simulation with a retrograde disky satellite at an inclination of 30 degrees is shown in the top left panel. This case is also discussed throughout the rest of this thesis. All stars are selected to be within a cylindrical shell with 1 < |z/Z0| < 3 and 2 < R/RD < 3, where Z0 and RD are the scale height and scale radius of the host galaxy given in Table 2 (see also Sales et al., 2009).
14 3.4 Eccentricity 3 RESULTS
Figure 13: Stacked histogram of the stellar eccentricity distribution for diﬀerent simulations. The stars are selected to be within a cylindrical shell at t = 10 Gyr. The particles have a height of 1 < |z/Z0| < 3 above the plane of the host disk where Z0 is the scale height of the host. The stars also have cylindrical radial distances of 2 < R/RD < 3 where RD is the scale length of the host. Both the scale height and length are given in Table 2. The histograms are scaled to reﬂect the relative masses of the host and satellite. Host stars are shown in blue and satellite stars are shown in orange.
Figure 14 shows the eccentricity distribution at diﬀerent heights above the, for the case of a retrograde disky satellite at an inclination of 30 degrees. It shows that at higher z, the eccentricity of the host tends to be lower while the eccentricity of the satellite tends to be higher.
Figure 14: Stacked histogram showing the dependence on height above the plane at t = 10 Gyr. The ﬁgure assumes the case of a retrograde disky satellite at an inclination of 30 degrees. Like in Figure 13, the stars have cylindrical radial distances of 2 < R/RD < 3 with respect to the host galaxy where RD is the scale length of the host given in Table 2. The histogram is also scaled by mass to portray the relative mass contributions of the satellite and the host. Host stars are shown in blue and satellite stars are shown in orange.
15 3.4 Eccentricity 3 RESULTS
Figure 15 shows two velocity diagrams color coded by eccentricity. This ﬁgure and its character- istics will be discussed in more detail in the next Section.
Figure 15: Velocity distributions at t = 10 Gyr of the stars of the satellite galaxy. The stars are color coded by their eccentricities. The system is aligned with the disk of the host and the stars are selected to be within a sphere with radius 2.5 kpc at a galactocentric distance of x = 2.4RD. Here, RD is the scale length of the host galaxy given in Table 2. The system is again scaled by a factor 1.5, since the simulation used a smaller scale length for the host galaxy than that of the Milky Way.
16 3.5 Eccentricity and angular momentum 3 RESULTS
3.5 Eccentricity and angular momentum
Figure 16 shows density plots of the eccentricity versus angular momentum for stars of the satellite galaxy for four diﬀerent simulations. In each panel, the angular momentum is calculated at t = 10 Gyr with respect to the reference frame of the host disk. The ﬁducial simulation (retrograde disky, 30 degrees) is shown in the top left panel. The density plots show various substructures and some clear diﬀerences between the various simulations are visible. Every simulation features a relatively sharp cut-oﬀ at high eccentricities, though for the spherical simulation (top right panel) it is more diﬀuse for very negative Lz. This −1 cutoﬀ bends oﬀ at roughly |Lz| > 500 Mpc km s . Both of the retrograde disky simulations (top left and bottom right panels) show two highly retrograde extensions.
Figure 16: Density plots of the angular momentum and eccentricity of satellite stars after 10 Gyr. The four panels show the results for diﬀerent simulations. The angular momentum is calculated in the reference frame of the host at t = 10 Gyr.
To understand the diﬀerent structures present in these diagrams, we focus in more detail on the top left panel (i.e. our default simulation). In Figure 17, several locations have been selected which are marked with numbers 1 to 5. The stars are color coded by their distance to the center of the satellite in the ﬁrst snapshot available, as shown in Figure 18. We can clearly see that stars in the various regions originate from diﬀerent locations in the satellite. For example, stars with high eccentricities mostly come from large distances. Furthermore, the stars in selection 4 originate from smaller radial distances compared to stars with similar angular momentum. Note however that if the stars are selected to be within a sphere at solar distance, the features in the diagram are less clear. These ﬁgures also help us understand the features seen in Figure 15. They show for example that stars with large negative vφ have lower eccentricities.
17 3.5 Eccentricity and angular momentum 3 RESULTS
Figure 17: Distribution of the angular momentum versus eccentricity of the satellite galaxy at 10 Gyr. The stars are color coded by their distance from the center of mass at the time of the ﬁrst snapshot that it available. 5 selections are marked which can be easily distinguished by their diﬀerences in initial radial distances. In the right panel the stars are selected to be within a sphere of radius 3 kpc from the solar position.
Figure 18: Initial positions of the stars. The host stars are colored in dark blue while the stars from the satellite galaxy are color coded by distance to the center of the satellite galaxy. The system is aligned with the satellite galaxy.
The reason for these trends becomes even clearer in Figure 19, where I plot with diﬀerent colours the stars selected in the various regions of Figure 17 (left panel). Stars from selection 1 (cyan) are located almost exclusively at the central region with the majority within 3 kpc from the center. Stars from selection 3 (green) originate from relatively high radial distances but are located close to the host just before the merger. Stars from selection 4 are located in a ring structure within r < 4 kpc, with some outliers trailing the satellite. Meanwhile, stars from selection 5 (orange) are located almost exclusively at the outer parts of the satellite.
18 3.5 Eccentricity and angular momentum 3 RESULTS
Figure 19: Spatial distribution of stars in the satellite galaxy at the time of the ﬁrst available snapshot. The satellite stars are shown in black. Stars from selection 1 are highlighted in cyan, 3 in green, 4 in red and 5 in orange. Selection 2 is omitted for clarity. The host galaxy is located in the top left corner in dark blue.
Figures 20 and 21 show the position of the particles in the selections until 0.45 Gyr. In the xy plane shown in Figure 20, the satellite galaxy orbits counterclockwise. In the ﬁrst 0.2 Gyr, the satellite as a whole has undergone roughly half an orbit around the host. At t = 0.3 Gyr, it becomes clear that selections 1 and 3, which are shown in cyan and green respectively, are in leading orbits. The particles from selections 4 and 5, shown in red and orange, are in trailing orbits. The trailing particles are swept out and separated from the leading particles during the ﬁrst two encounters with the galaxy.
Figure 20: Spatial distribution of stars from the stars in the satellite galaxy over time. Again, the satellite galaxy is shown in black and the host galaxy is shown in blue. Stars from selection 1 are highlighted in cyan, 3 in green, 4 in red and 5 in orange. Selection 2 is omitted for clarity.
19 3.6 Metallicity 3 RESULTS
Figure 21: Spatial distribution of stars from the stars in the satellite galaxy over time. Again, the satellite galaxy is shown in black and the host galaxy is shown in blue. Stars from selection 1 are highlighted in cyan, 3 in green, 4 in red and 5 in orange. Selection 2 is omitted for clarity.
Now that we know where the stars from the satellite galaxy could originate from depending on their angular momentum and eccentricity, we can start to look for methods to validate this hypothesis for Gaia-Enceladus. As the stars originate from diﬀerent parts of the satellite galaxy, we can expect them to have diﬀerent formation histories. The formation history of a star can be traced back using the abundances of metals that the star has. Thus if we look for diﬀerences in the metal abundance of stars with diﬀerent angular momentum and eccentricity, we can validate whether they actually have diﬀerent origins.
The metallicity is mostly a function of distance to the center of the galaxy. A useful parameter therefore is the metallicity gradient ∆Z/∆r, which gives a typical change in metallicity Z for a change in galactocentric distance r. It is usually given in units of dex kpc−1 where 1 dex equals a diﬀerence of one order of magnitude in Z. Ho et al. (2015) has measured the metallicity gradients 8 49 nearby starforming galaxies. For a galaxy with a stellar mass M ≈ 6 × 10 M , I estimate using their results that the metallicity gradient is approximately ∆Z/∆r ≈ −0.05 dex kpc−1. Thus, for every kpc from the center of the galaxy, the metallicity Z is multiplied by a factor 10−0.05 = 0.89. If we assume that we can apply the same metallicity gradient to Gaia-Enceladus, then we can use the initial radial distances to ﬁgure out the expected diﬀerence in metallicities. In Figure 17, the mean initial radial distances of selections 1, 4 and 5 are roughly 1, 4 and 10 kpc respectively. Thus the expected metallicity diﬀerences between 1 and 4 would be ∆Z/∆r ≈ 3 kpc · −0.05 dex kpc−1 ≈ −0.15 dex. The diﬀerence in metallicity between 4 and 5 would be ∆Z/∆r ≈ 6 kpc · −0.05 dex kpc−1 ≈ −0.3 dex.
20 4 Discussion
The aim of the thesis has been to characterize the stars from a satellite galaxy in a minor merger. This may help to ﬁnd likely members of Gaia-Enceladus in the future, especially at larger distances from the Sun. We expect stars that were lost earlier on to be located at larger distances and have more negative angular momentum, so even more retrograde orbits than the Gaia-Enceladus stars that populate the solar neighbourhood. One of the most important simpliﬁcations of this simulation is that it does not consider gas physics nor star formation. The gas could act as a stabilizing component because the orbital energy of the stars will heat up the gas. This heat can then be radiated away and the energy that is lost in the process would cause less disturbances in the structure of the thick disk (Robertson et al., 2006). This could have quite signiﬁcant inﬂuence on the morphology and kinematics of the ﬁnal system. Lastly, the scale lengths that are used in the simulation are 35% smaller than that of the Milky Way (Villalobos and Helmi, 2009). In some cases, the system is therefore scaled by a factor 1.5 so that it would resemble the Milky Way. This may be too much of a simpliﬁcation however, as some of the properties of the system may not scale in the same way. However this cannot be easily solved, because the simulation also does not include a thin disk, whose growth will aﬀect the properties of the merger remnant (Villalobos et al., 2010).
21 5 Summary and conclusion
In this thesis I have carried out N-body simulations of a minor galactic merger, resuming the simulations of Villalobos and Helmi (2009). I ﬁnd that the previous results are still largely appli- cable after 10 Gyr; stars from the host and satellite are still distinguishable by their velocities and angular momenta. Between 1 and roughly 3 Gyr from the start of the simulation, several shells are visible. These shells emerge when a collections of stars have similar apocenters. When these stars are near their pericenter, they form streams passing through the central region of the galaxy. These streams can be observed for roughly 6 Gyr. After 10 Gyr, the stars from the host galaxy are distributed in a disk, while the stars from the satellite galaxy are distributed more spherically. Iorio and Belokurov (2019) ﬁnds that RR Lyrae stars from the inner stellar halo are distributed in an elongated shape in the xy plane. From this they conclude that the ex-situ halo stars were deposited in a single large merger event. However, this is inconsistent with the results from this simulation. At 4 Gyr years from the start of the simulation, the satellite stars are distributed quite smoothly but in an elongated shape. During the rest of the simulation, the satellite stars become more symmetrically distributed. Thus, if the merger with Gaia-Enceladus happened roughly 10 Gyr ago, it would not produce an elongated structure in the galactic plane. This inconsistency could be the result of a selection eﬀect impeding the ability to identify RR Lyrae stars in the Gaia DR2 data (see also Helmi et al., 2018). The main properties of the Toomre diagram seen after 4 Gyr by Villalobos and Helmi (2008) are roughly maintained after 10 Gyr and resemble those found in the Gaia data (Figure 2). The arch shaped feature at vφ < −300 km/s is present during the whole simulation. However, it is only at speciﬁc times that the arch is clearly deﬁned. At larger galactocentric distances, the stars from the satellite are more clearly separated in their kinematics as they have a more retrograde motion. This results in a separation in vφ and Lz between the stars from the host and satellite galaxy. Whereas the distribution of angular momentum over radial distance shows some substructures at t = 4 Gyr, the distribution is quite smooth at t = 10 Gyr. Interestingly, we ﬁnd that stars from the satellite galaxy show two peaks around = 0.5 and = 0.9 at the ﬁnal time. Particles with low eccentricities were mostly located near the center of the satellite, which because of dynamical friction decayed leading to circularization, while the highly eccentric particles were in trailing orbits. An interesting result is that the satellite stars show a correlation between their current angular momentum and eccentricity and their location at the time of the merger. Thus the angular momentum combined with the eccentricity can tell us more about the origins of stellar populations. Especially particles with eccentricities around = 0.5 and relatively small angular momenta −1 (Lz > −500 kpc km s ) seem to have a common origin. At the time of the ﬁrst available snapshot, these particles are mostly located within 3 kpc from the center of the satellite galaxy. In the case of a disky, retrograde satellite launched at a 30 degree inclination, another group of stars can be distinguished. This group, which has a similar eccentricity but a more negative Lz, is located at slightly larger galactocentric distances of about 4 kpc in the ﬁrst available snapshot. They form a ring structure around the central regions with some outlying clumps trailing the satellite. As the composition of a star also largely depends on its place of origin, we can expect to see some diﬀerences in metallicity and abundances. If the satellite galaxy had a metallicity gradient at the time of the merger, the metallicity should thus be correlated to the eccentricity and angular momentum. Assuming that Gaia-Enceladus initially had a metallicity gradient of −0.05 dex kpc−1, the diﬀerence in metallicity between the selections in Lz and should be of the order of 0.15 to 0.3 dex.
22 5 SUMMARY AND CONCLUSION
Myeong et al. (2019) proposes that, the Milky Way had a merger with another large galaxy. Besides Gaia-Enceladus, which they coined the Sausage, they suspect that the Milky Way also merged with a smaller galaxy named Sequoia. In this scenario, Gaia-Enceladus is mostly responsible p 2 2 for the stars in the most radial orbits (high Vx + Vz ) with typical eccentricities of ≈ 0.8. The Sequoia galaxy is responsible for the most retrograde moving stars (most negative Vy) which have lower eccentricity. The results in this thesis show that stars with very retrograde motions −1 (Lz ≈ −1500 Mpc km s ) and lower eccentricities could originate from the very outer parts of Gaia-Enceladus (the leading arms). Meanwhile, stars with slightly radial orbits most probably originate from the inner parts. This could partly explain the diﬀerences in abundance between Sequoia and the Gaia-Enceladus which is claimed by Myeong et al. (2019).
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