Phase spirals in cosmological simulations of Milky Way size galaxies.

• Gaia Data Release 2 (2018): the Milky Way's disk is perturbed, and presents phase spirals in the Z - 𝑉_Z plane (Antoja et al. 2018) of the solar neighborhood.​
• The phase spirals are present in the Z - 𝑉_Z plane of a local region of the galactic disk and are the consequence of a phase mixing process triggered by external or internal perturbation which causes vertical and radial oscillations. ​
• Spiral shape that winds up over time: Also can be seen when coloured by 𝑉_ϕ and 𝑉_𝑅.

An interacting satellite can induce an energy kick and trigger phase mixing event.

This spiral pattern is compatible with the last pericenter of the Sagittarius Dwarf Galaxy estimated at 500 Myr ago.

Since Gaia DR2, the phase spirals as consequence of Sagittarius have been studied in isolated models (N-body).

We use a MW-size GARROTXA model (a hydrodynamical zoom-in cosmological simulation).

• Spatial resolution of 100 pc.​
• Minimum mass of 10³ 𝑀_⨀ for star particles and 10⁵ 𝑀_⨀ for dark matter particles.​
• Minimum timestep 10³ years.​
• Mass assembling history similar to Milky Way.​

Stellar particles with ages between 0 and 5 Gyr.
Galactocentric radii from 10 to 12 kpc and vertical position |𝑍 | < 2.5 kpc.
12 adjacent sectors spanning 30 deg in 𝜙
Temporal evolution from lookback time of 6 to 0 Gyr.

We use Rockstar halo finder  to identify all sub-halos that may impact the disk’s kinematics.

In Table 1 we summarize the characteristics of those which are more massive and reach lower distance to the main galaxy over the timespan studied.

• The formation of the stellar thin disk in our model is enhanced at 9 Gyr by  several pericenters,  and it remains almost permanently disturbed by the many following interactions with the satellites.
• We can see that the phase spiral becomes more perceptible around the 4 Gyr (complete figure in García-Conde et al 2022.)

• In Fig. 3 we explore the vertical phase space structures as a function of radius for a single azimuth. We see that the global distribution changes from elongated in V_Z axis at small radii to elongated in 𝑍 in the outer disc.
• This has been detected in the Gaia data (Laporte et al. 2019, Antoja et al. 2023) and is a consequence of the smaller restoring vertical force in the outer parts of the disc.
• The phase spiral becomes detectable at radii larger than 6 kpc and is present up to very large radius, showing that they are not exclusive of the range of 10-12 kpc.
• The short vertical extent of the distribution at inner radii, combined with the limitations in resolution, may be hampering our ability to see clear structure there.

• We show in Fig. 4 seven stellar populations with increasing age, starting with the cold gas (< 8000 K) and newborn stellar particles.
• We see that the global phase spiral is more pronounced in stellar particles with ages of about 1−5 Gyr confirming the age analysis in Tian et al. (2018) and Bland-Hawthorn et al. (2019).
• Although there are some hints of structure in the older groups, it definitively fades out for particles older than 5 Gyr.
• This is due to younger stars being dynamically colder, thus reflecting more prominently the effects of perturbing phenomena. Also, as described in Li & Shen (2020), groups of older stars whose orbits are kinematically hot have a larger range of vertical frequencies, which may blur the phase spiral.
• We note here that the spiral pattern observed in the 𝑉_𝜙 -weighted maps (central row) differs from one age population to another (e.g. the 2 − 3 Gyr group vs. the 3 − 4 Gyr one). This result suggests that different stellar populations may have been perturbed and/or phase mixed differently.
• Finally, we see that the very young stellar particles (less than 1 Gyr) are found in groups that do not fully cover the phase space but present some sort of spiralility.
• The cold gas appears to be distributed in non-isotropic phase space patterns and the newborn stellar particles (black dots) are not born close to 𝑍 ∼ 0 and 𝑉_𝑍 ∼ 0. This will lead to subsequent phase mixing of the young populations which could create the thin spirals in the vertical phase space projection.

• In this work we detect phase spirals at multiple times and locations, but it is not trivial to distinguish the moment of their appearance.
• A phase spiral will present a high amplitude of the m=1 mode in the 𝑍-𝑉_𝑍 space (or m=2 mode if two-armed).
• We also take into account angle variation (to ensure a spiral shape) and m=1 dominating over higher mdoes (more details in García-Conde et al 2022).

• We observe a coincidence between the phase spirals and pericenters.
• The maximum strength of the gravitational pull of our satellites remains rather constant with time, in contrast with an interaction with a Sagittarius-like system, where every new pericentre induces a larger kick in velocity than the previous one, making it easier to “overwrite” the existing phase-space substructure.
• We have multiple pericenters (of different satellites) that appear naturally in our simulation. This, combined with the fact that in our model dynamically cold stars are being formed all along the evolution of the galaxy, results in different stellar populations responding differently to the new perturbations, which is something not captured by isolated models without star formation and gas.

• Other possible perturbative mechanisms: highly anisotropic distribution of dark matter left over from the satellites, multiple dark subhalos, misalignment between disc and halo, resonances, and the presence of non-axisymetric structures in the disc.
• These mechanisms are currently under study with this simulation (García-Conde et al in prep).

• The combination of the acceleration of the different components of the simulation are of special interest to understand this behaviour of the disk.
• The possibility of connecting local dynamical phenomena with global perturbations from satellites, gas behaviour and star formation processes in the same model in the context of a cosmological simulation is definitively a promising future avenue of work that we open in García-Conde et al 2022.
• We will study these velocity substructures in other cosmological simulations with Milky Way -like models and with different codes (RAMSES).

• We can still not claim a perfect match between the phase spirals observed in the Gaia data and the ones found in our model.
• These spirals are present throughout the last several Gyr of the evolution, suggesting that this phenomenon might be common in the life of certain galaxies.
• The spirals are more notable for younger to intermediate-age stars and are especially prominent near pericenter passages of the three main galaxy satellites.
• These passages coincide with the times of star formation enhancements, an effect that has already been directly related to accretion events.
• Recent studies modeling Sagittarius as the main perturber estimate its mass as ≳ 10¹⁰ M_⊙ at the time of impact, more especifically,  6 · 10¹⁰ and 2 · 10¹⁰ M_⊙  in Laporte et al. (2019) and Bland-Hawthorn & Tepper-García (2021) , respectively.
• Our satellites seem to belong to the low mass regime, and the pericenter distance of our heaviest satellites is larger than the ones of recent Sagittarius pericenters (the effects of our perturbers should be far less strong), yet we do observe phase spirals and a correlation between pericenters and the strength of the phase spirals.
• This can be attributed to other collective effects (García-Conde et al in prep),  such as the dark matter structures or gas misalignment can also play an important role in the vertical behavior of the galaxy.
• Our model pericenters get synchronized over time, and there is a combined mass of up to ∼ 10⁹ 𝑀_⊙ by the time they start affecting the disc.

References

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