Taking the Milky Way for a spin: disc formation in the ARTEMIS simulations

We investigate the formation (spin-up) of galactic discs in the ARTEMIS simulations of Milky Way-mass galaxies. In almost all galaxies discs spin up at higher [Fe/H] than the Milky Way (MW). Those that contain an analogue of the Gaia Sausage-Enceladus (GSE) spin up at a lower average metallicity than those without. We identify six galaxies with spin-up metallicity similar to that of the MW, which form their discs $\sim 8-11$ Gyr ago. Five of these experience a merger similar to the GSE. The spin-up times correlate with the halo masses at early times: galaxies with early spin-up have larger virial masses at a lookback time $t_L=12$ Gyr. The fraction of stars accreted from outside the host galaxy is smaller in galaxies with earlier spin-ups. Accreted fractions small enough to be comparable to the MW are only found in galaxies with the earliest disc formation and large initial virial masses ($M_\mathrm{200c} \approx2\times10^{11}M_\odot$ at $t_L=12$ Gyr). We find that discs form when the halo's virial mass reaches a threshold of $M_\mathrm{200c}\approx(6\pm3)\times10^{11}M_\odot$, independent of the spin-up time. However, the failure to form a disc in other galaxies appears to be instead related to mergers at early times. We also find that discs form when the central potential is not particularly steep. Our results indicate that the MW assembled its mass and formed its disc earlier than the average galaxy of a similar mass.


INTRODUCTION
The Milky Way, like all other spiral galaxies, was not born with a rotating disc, it had to form one. Exactly when and how galaxies acquire stable stellar discs is an open question, currently pursued both with cutting-edge look-back observations and through theoretical and numerical calculations.
The ratio of the rotational velocity to the velocity dispersion / is measured to decrease significantly with increasing redshift for galaxies of a given stellar mass (see Kassin et al. 2012;Wisnioski et al. 2015).This disc settling is a mass-dependent process: more massive galaxies attain higher / values earlier (Wisnioski et al. 2019).Mixed in with these trends is the information on the disc emergence, i.e. the galaxy's transformation from a state characterised by random motions to a configuration dominated by a coherently rotating stellar disc.Currently, available samples of high-redshift galaxies with morphological and kinematic measurements are still too small to answer this question through population studies (but see recent studies by Ferreira et al. 2022Ferreira et al. , 2023;;Nelson et al. 2023;Jacobs et al. 2023;Robertson et al. 2023).However, in the Milky Way, archaeological records comprised of accurate kinematic information provided by Gaia (Gaia Collaboration et al. 2016) and detailed chemical abundances supplied by surveys such as APOGEE (Majewski et al. 2017) ★ E-mail: amd206@cam.ac.uk (AMD) and GALAH (De Silva et al. 2015) have recently been used to crack the puzzle of the disc emergence.
For example, Belokurov & Kravtsov (2022) show that the stars born in-situ in the Milky Way (separated from the accreted stellar debris using the abundance ratio of aluminium to iron [Al/Fe]) exhibit a characteristic trend of the increasing rotational velocity with metallicity [Fe/H].At low metallicity, i.e. at [Fe/H] < −1.3, the Milky Way stars possess little to no net spin, however from [Fe/H]≈ −1.3 to [Fe/H] ≈ −0.9, the median azimuthal velocity   rises from approximately ≈ 50 km/s to ≈ 150 km/s.Belokurov & Kravtsov (2022) associate this rapid spin-up with the emergence of the old Galactic disc, following the turbulent and chaotic state of the Galaxy imprinted in the ancient in-situ stellar population Aurora. 1 Whilst more contaminated in their selection of the in-situ population, the follow-up studies of Conroy et al. (2022) and Rix et al. (2022) report similar trends of the rotational velocity with metallicity.Belokurov & Kravtsov (2022) also highlight a discrepancy between the observations and the numerical simulations of galaxy formation.Whilst the spin-up itself is a ubiquitous feature in chemokinematic histories of model Milky Way-sized galaxies, the metallicity at which the disc forms in the two simulation suites analysed (Auriga and FIRE) is noticeably higher compared to the observa-tions.Similar results were also produced by McCluskey et al. (2023) using the FIRE-2 simulations, although one of these galaxies (named Romeo) does have a similar time of disc formation to the Milky Way.This question is further explored in Semenov et al. (2023a) using a larger sample of Milky Way-sized galaxies from the Illustris TNG50 simulation to study the statistics of the spin-up metallicity.They conclude that in TNG50 only ≈ 10% of Milky Way-sized galaxies form their disc at metallicities similar to that measured by Belokurov & Kravtsov (2022).They also show that the haloes of these galaxies assemble their mass early.
One of the most significant events in the Milky Way's history was the merger with Gaia Sausage-Enceladus (GSE; Belokurov et al. 2018;Helmi et al. 2018), a massive satellite of total mass ∼ 10 11  ⊙ which was accreted by the Milky Way 8-11 Gyr ago (e.g.Belokurov et al. 2018;Fattahi et al. 2019).This is observed as a population of stars in the stellar halo with highly eccentric orbits and relatively high metallicity.Milky Way analogues with GSE-like mergers have been studied in various suites of high resolution zoomed-in cosmological simulations, such as Auriga (Grand et al. 2017;Fattahi et al. 2019;Grand et al. 2020) and artemis (Font et al. 2020;Dillamore et al. 2022Dillamore et al. , 2023)).These have shown that approximately one third of Milky Way-like galaxies possess a dominant radially anisotropic feature in their stellar haloes resembling the GSE (Fattahi et al. 2019), and that the associated mergers have transformative effects on their host galaxies (Dillamore et al. 2022).These include creation of an in-situ stellar halo (Belokurov et al. 2020;Grand et al. 2020) and tipping of the disc (Dillamore et al. 2022;Orkney et al. 2023).
Following the above early attempts to gauge the conditions necessary for the disc emergence, in this study we focus on the connection between the disc spin-up in model Milky Way-like galaxies and their mass assembly histories using the artemis simulation suite.This paper is arranged as follows.We briefly describe the artemis simulations in Section 2 and our methods in Section 3. Our results are presented and discussed in Section 4, and summarised in Section 5. Finally, in Appendix A we show the star formation density of a selection of artemis galaxies across time to illustrate the changes in morphology involved in disc formation.

SIMULATIONS
artemis (Font et al. 2020) is a zoomed-in hydrodynamical simulations suite, consisting of 45 haloes with Milky Way-like masses.Details can be found in Font et al. (2020) and are outlined below.
The simulations were run using the Gadget-3 code (Springel 2005) in a WMAP ΛCDM cosmology.While the hydrodynamics code and subgrid physics are shared with the eagle project (Schaye et al. 2015;Crain et al. 2015), the stellar feedback was recalibrated to better match the stellar mass-halo mass relation (Font et al. 2020).
An initial collisionless simulation was run to redshift zero in a base periodic box of side length 25 Mpc ℎ −1 .A set of 45 galaxies was then selected based purely on their virial masses.These lie in the range 0.8 <  200c /10 12  ⊙ < 2.0 at redshift  = 0, where  200c is the mass enclosed within a volume containing a mean density of 200 times the critical density.
The size-stellar mass relation of the artemis galaxies closely matches the observations by Shen et al. (2003) in the SDSS survey (Font et al. 2020).However, the typical disc masses of the artemis galaxies are ≈ 10 10  ⊙ , smaller than the estimate for the Milky Way of ≈ (5 ± 0.5) × 10 10  ⊙ (e.g., McMillan 2017).

Selection of disc galaxies
We define a disc galaxy using the corotation parameter  co (Correa et al. 2017), the fraction of stellar kinetic energy associated with motion in the positive sense about the -axis.Specifically, where   is the mass of star particle , while  , and   are its -angular momentum and projected galactocentric radius in the - plane respectively.The sum is over all particles with  < 30 kpc and positive angular momentum (i.e.circulating in the same sense as the net rotation). is the total kinetic energy of stars with  < 30 kpc.
In Dillamore et al. (2022) we defined a disc galaxy using threshold  co ≥ 0.4 (Correa et al. 2017), and used this method to identify 27 of the 45 artemis galaxies with discs at the present-day.In this study, we use a stricter threshold of  co ≥ 0.5, which removes the borderline cases of weak discs and retains only galaxies in which more than half of the stellar kinetic energy is associated with net rotation.This results in a sample of 18 galaxies which we use in this study.In three of these  co decreases below 0.5 before recovering to exceed it again after  spin .There are also 17 examples of galaxies where  co ≥ 0.5 at some earlier snapshot but not at the present day.We include these in Fig. 2.
Since  co defines the presence of a stellar disc, we also use it to define the lookback time of disc emergence or spin-up time,  spin .We let  spin be the lookback time of the earliest snapshot at which  co ≥ 0.5.Since  co takes into account all stars present within  = 30 kpc at a particular snapshot, this should be seen as the time at which the galaxy becomes disc-dominated rather than when the disc starts forming.We therefore find that star formation in a disclike configuration generally begins a few snapshots (or ≈ 1 − 2 Gyr) before  spin , as can be seen in Figure A1 in the Appendix.We also note that this figure shows that, generally, stars born before disc formation have very irregular distribution, consistent with results of Belokurov & Kravtsov (2022, see their Fig.12) based on the FIRE-2 simulations.Thus, simulations do not show the existence of 'ancient' low-metallicity discs before the actual disc spin-up at metallicities [Fe/H] ≳ −1.5.

Selection of the GSE sample
In Dillamore et al. (2022) we identified artemis galaxies containing a feature resembling the Gaia Sausage-Enceladus (GSE) in their accreted stellar halo.This selection process is briefly described below; see Dillamore et al. (2022) for full details and discussion of the fitting procedure.
Particles in artemis are classed as in-situ if they were born bound to the host subhalo, defined as the most massive subhalo identified by the SUBFIND algorithm (Dolag et al. 2009) at each simulation snapshot.They are otherwise classed as accreted.
We calculate the velocity components in spherical coordinates of accreted stars in a Solar neighbourhood-like region (5 <  [kpc] <  15, 0 < || [kpc] < 9) in each galaxy at the redshift  = 0 snapshot.A two-component Gaussian mixture model is fitted to these velocity distributions using the expectation-maximization algorithm Gaus-sianMixture from the scikit-learn library (Pedregosa et al. 2011).
All stars within the above cuts are included in these fits.The two Gaussian components represent a radially anisotropic and a more isotropic distribution.The radial anisotropy is characterised by the anisotropy parameter 2008).For the observed GSE feature in the Milky Way,  ≈ 0.86 (Fattahi et al. 2019).
We include a halo in our GSE sample if the more anisotropic (higher ) Gaussian component has  > 0.8 and a contribution to the accreted Solar neighbourhood population of greater than 40%.This follows a similar criteria used by Fattahi et al. (2019).The GSE sample therefore consists of galaxies with significant, highly radial features in their accreted haloes.This gives us a total of 23 galaxies in the GSE sample, 10 of which also have  co ≥ 0.5 at the present-day.
Our final sample of 18 disc galaxies therefore contains 10 GSE galaxies.We refer to the remaining 8 as non-GSE galaxies; these are galaxies with  co ≥ 0.5 at the present-day but no GSE-like feature.

Rotational velocity, age and [Fe/H]
We follow Belokurov & Kravtsov (2022) and Semenov et al. (2023a) and investigate the relations between the median azimuthal velocity   , age and [Fe/H] of stars in the solar neighbourhood.We work in a coordinate system with its -axis aligned with the total angular momentum of stars within  = 30 kpc of the galactic centre.We select stars from the redshift  = 0 snapshot from the region 5 <  [kpc] < 11, || < 3 kpc which are flagged as in-situ in origin.To correct for the metallicity differences between different galaxies, we subtract the median [Fe/H] of each sample such that the corrected median [Fe/H] is zero in each galaxy.This means that the median solar neighbourhood metallicities approximately match that of the Milky Way (Haywood 2001).
For  Belokurov & Kravtsov (2022) found that the transition from low to high   (spin-up) generally occurs at higher metallicities in the FIRE simulations than in the Milky Way (except for the galaxy in the Romeo halo; see McCluskey et al. 2023).The middle panel of Fig. 1 shows that this is also true in the artemis galaxies, with a median   = 150 km/s occuring at [Fe/H] ≈ −0.5 compared to -1 in the Milky Way.However, there is a difference between the GSE and non-GSE samples.The galaxies which spin up at lower metallicities and earlier times are more likely to contain a GSE analogue, whereas the median   of the non-GSE galaxies spins up at later times and higher metallicities.
From the middle panel we select six galaxies which have the most Milky Way-like   vs [Fe/H] tracks, henceforth 'early spin-up galaxies'.These are the six galaxies with the highest median   at [Fe/H] = −1, five of which are in the GSE sample.The tracks of these galaxies are shown with dotted lines in each panel of Fig. 1.The left panel confirms that they do indeed spin up at earlier than average times, reaching a median   ∼ 150 km/s by   ∼ 10 Gyr.

Spin-up times and evolution of haloes and their mass concentration
We show the relation between the spin-up time  spin and the galaxies' masses at early times in Figure 2. The top and middle panels show the virial mass  200c and maximum circular velocity  max respectively, both calculated at a lookback time of   = 12 Gyr.The galaxies with discs ( co ≥ 0.5) at the  = 0 snapshot are shown by circles, with the early spin-up galaxies selected from Figure 1 shown by circles with black edges.We also show galaxies where  co exceeds 0.5 at some earlier snapshot, but is less than 0.5 at the present-day  Here we also show galaxies with  co ≥ 0.5 at earlier snapshots only, but not at the present-day ('former discs'; crosses).Red (blue) points indicate haloes in the (non-)GSE samples, and the early spin-up galaxies selected from Fig. 1 are marked with black rings.Middle panel: as above, but showing the maximum circular velocity  max (at   = 12 Gyr) against  spin .In both cases there is a correlation with spin-up time, with earlier spin-ups occurring in galaxies with higher masses and circular velocities at   = 12 Gyr.Bottom panel: fraction of accreted stars within  = 30 kpc at the present-day against spin-up time.An estimate and its uncertainty for the Milky Way is shown with a black line and grey band.Disc galaxies with earlier spin-ups tend to have lower accreted stellar fractions, while the former discs (crosses) have much larger proportions of accreted stars.In each snapshot all accreted stars present in the host galaxy at that time (within 30 kpc) are included in the calculations.The lines and bands have the same meanings as in Fig. 1.At   < 11 Gyr the non-GSE galaxies have a higher median fraction of accreted stars, with a median of about 30% at   = 10 Gyr.With one exception the early spin-up galaxies generally have low accreted fractions (≲ 0.1).
('former discs', marked with crosses).There is a moderate correlation between  spin and both the virial mass and  max at   = 12 Gyr, with earlier spin-ups occurring in galaxies with larger  200c (  = 12 Gyr) and  max (12 Gyr).In particular, the early spin-up galaxies have both larger  200c (12 Gyr) and  max (12 Gyr) than almost all other presentday disc galaxies.
There is a large number of non-GSE galaxies with  spin between 6 and 10 Gyr and  200c (12 Gyr) ≲ 10 11 M ⊙ , lower than the  200c (12 Gyr) values of early spin-up galaxies' masses.This is likely related to the different accretion histories of the GSE and non-GSE galaxies.We previously showed (Dillamore et al. 2023) that the artemis galaxies lacking a GSE analogue undergo more massive mergers than those with a GSE-like feature, many of which happen late.Their typical accreted satellites have stellar masses of ∼ 10 10  ⊙ , roughly four times larger than those of GSE galaxies.This means that a greater proportion of the galaxies' final mass is assembled after   = 12 Gyr.Hence to reach a final halo mass within the artemis selection criteria, these galaxies typically have lower masses at early times than those with a GSE analogue.
To show how accretion history relates to the spin-up time, we calculate the fraction of stars within  = 30 kpc which are classed as accreted.This is plotted against  spin in the bottom panel of Figure 2.For comparison, we calculate an estimate of the Milky Way's accreted fraction as follows.We take the measurement of the Milky Way's total stellar mass by McMillan (2017),  ★ = (54.3± 5.7) × 10 9  ⊙ , and the total stellar halo mass from Deason et al. (2019),  ★ halo = (1.4±0.4)×10 9  ⊙ .We assume that a fraction  acc,halo = 0.81 of the stellar halo is accreted (Naidu et al. 2020), and calculate our estimated overall accreted fraction  acc =  halo,acc  ★ halo / ★ = 0.021 ± 0.006.This estimate and its uncertainty are shown in the bottom panel of Figure 2 by the black solid line and gray shaded region.Since this calculation assumes that all accreted stars are in the halo, we have checked that our results do not significantly change if we exclude accreted stars on disc-like orbits in the simulations.
For the present-day disc galaxies, the galaxies with earlier spinups tend to have smaller accreted stellar fractions.A large majority of the artemis galaxies have accreted fractions significantly larger Former discs The panel shows that disc in the artemis galaxies form when their haloes reach mass of  200c ≈ (6 ± 3) × 10 11  ⊙ .Bottom panel: the ratio of the circular velocity  c = [  tot (<  )/ ] 0.5 at the stellar half-mass radius  eff to that at 3 eff , which we use as a measure of mass concentration and steepness of the potential.The panel shows that discs in the artemis galaxies generally form when the mass is not very centrally concentrated ( c ( eff )/ c (3 eff ) < 1), but the mass distribution becomes centrally concentrated after the disc forms.The former disc galaxies generally behave similarly to the present-day discs.
than that of the Milky Way.The exceptions (G19, G38 and to a lesser extent G34) all have early spin-ups ( spin > 9 Gyr) with Milky Waylike   vs [Fe/H] relations (see Fig. 1).The former disc galaxies (mostly lacking a GSE feature) tend to have larger accreted fractions, including those with early spin-ups.This suggests that mergers are responsible for destroying these discs, and is consistent with the conclusions of Dillamore et al. (2023) that non-GSE galaxies on average undergo more major mergers.
In Figure 3 we show how the total accreted stellar fractions change across lookback time.At each snapshot, we calculate the fraction of all stars within  = 30 kpc which have been accreted before that time.The medians and 16th-84th percentile ranges are plotted vs. lookback time   for the GSE and non-GSE present-day disc galaxy samples, as well as individually for the six early spin-up galaxies.The GSE galaxies have lower median accreted fractions at all times after   ≈ 11 Gyr.The non-GSE galaxies have much larger contributions from accreted stars, peaking at ≈ 0.3 at   = 10 Gyr.This is likely Former discs 0.00 0.25 0.50 0.75 a reflection of their more active accretion histories (Dillamore et al. 2023).Five of the six early spin-up galaxies have small accreted fractions across all ages, at ≲ 0.1 at most snapshots.Finally, we note that the median accreted fractions of ∼ 0.1 − 0.3 are roughly consistent with the results of Semenov et al. (2023a).
In the top panel of Figure 4 we show the evolution of the virial mass  200c with lookback time   for the 18 present-day disc galaxies.We mark the spin-up times and corresponding virial masses with coloured points.The 16th-84th percentile range of the former discs is also shown as a function of time.The bottom panel of Figure 4 shows the ratio of the circular velocity  c ≡ [  tot (< )/] 1/2 at the stellar half-mass radius,  c ( eff ), and  c (3 eff ), again marking the corresponding values at the disc spin-up.In Hopkins et al. (2023, see their Figs. 6 and 7) the galaxies that form gas discs all have  c ( eff )/ c (3 eff ) ≳ 1 at the present-day, and mass concentration (represented by the shape of the circular velocity profile) was used as a measure of the steepness of the central potential.
Figure 4 shows that the virial masses at spin-up span a rather narrow range of ∼ 3 − 9 × 10 11  ⊙ , considerably smaller than the range of masses  200c (  = 12 Gyr) in Figure 2.Moreover, there is no apparent trend of  200c ( spin ) with  spin .This indicates that in the artemis simulations discs in  200c ( = 0) ≈ 10 12  ⊙ haloes form when their host halo reaches  200c ≈ (6 ± 3) × 10 11  ⊙ .We see this more clearly in the top-left panel of Fig. 5, where we plot  200c vs  co for each individual present-day disc galaxy. co remains small Total accreted stellar fraction Figure 6.Various quantities against lookback time   for galaxies with discs ( co ≥ 0.5) in any snapshot (green) and those which never form discs ( co < 0.5 in every snapshot, purple).From top to bottom, the panels show the corotation parameter  co , virial mass  200c , circular velocity ratio and total accreted stellar fraction (as shown in Fig. 3).Apart from  co itself, the most striking difference between the two samples is the larger fraction of accreted stars at early times in the non-disc galaxies.This suggests that the failure to form a disc may be due to merger events.
(< 0.3) while  200c increases from ∼ 10 10  ⊙ to ∼ 10 11  ⊙ , but increases and crosses  co = 0.5 when  200c ≈ (6 ± 3) × 10 11  ⊙ .Interestingly, this virial mass value is close to the mass threshold at which a hot halo forms and gas accretion transitions from cold-mode to hot-mode accretion (Kereš et al. 2005(Kereš et al. , 2009;;Dekel & Birnboim 2006;Dekel et al. 2009).Thus, this result is consistent with the scenario in which a hot halo is essential for disc formation by mediating the accretion of gas (e.g., Dekel et al. 2020;Stern et al. 2021;Hafen et al. 2022).Indeed, Figure 12 in Semenov et al. (2023b) shows that a hot gaseous halo forms over a significant fraction of the virial radius immediately before disc spin-up.
At the same time, the bottom panel of Figure 4 shows that disc spin-up generally occurs when  c ( eff )/ c (3 eff ) < 1 -i.e., when the mass distribution was not particularly centrally concentrated.This is also seen in the lower panels of Fig. 5, where the circular velocity ratio is plotted as a function of  co .This result is consistent with findings of Semenov et al. (2023b, see their Figs. 7, 8 and 9) that the mass distribution becomes more concentrated after the disc forms and that halo mass at spin-up has a narrower range than their mass concentration indicator.
We note that all discs have  c ( eff )/ c (3 eff ) ≳ 1 by  = 0, in agreement with findings of Hopkins et al. (2023), who found that all simulated galaxies that form a disc have  c ( eff )/ c (3 eff ) ≳ 1 at  = 0 (see, e.g., their Figs.4-7). Figure 4, however, shows that the mass concentration increases both before and after the disc forms and is thus not a cause of disc spin-up.Hopkins et al. (2023) also showed that a gas disc can form in a halo with  = 0 mass of  200c = 4 × 10 10  ⊙ (their m11a object), which is well outside the range of  200c ( spin ) = (6 ± 3) × 10 11  ⊙ found in the artemis simulations and the virial mass threshold expected for the hot halo formation.Nevertheless, this does not necessarily imply a discrepancy.Hopkins et al. (2023) focus on the formation of gas discs which may not necessarily lead to the formation of a stellar disc.Our definition of a disc, on the other hand, is based purely on stellar kinematics.Our findings are therefore not inconsistent with the formation of gas discs in dwarf galaxies.In fact, Hopkins et al. (2023) also find that at the time of formation of gaseous discs the circular velocity is decreasing with decreasing radius at  < 3 eff and increases generally after disc formation due to the growth of central mass concentration.If stellar discs were also found to be present in lower mass galaxies, this may indicate that a hot gaseous inner halo mediating gas accretion and inducing disc formation may form in different ways.It may form when the host halo has a regular mass concentration and reaches a threshold of  200c ( spin ) = (6 ± 3) × 10 11  ⊙ or it may form in haloes of lower virial mass if a strong central mass concentration capable of compressing gas to a sufficiently high temperature forms via some physical process.
These possibilities warrant further investigation.Our results, however, indicate that regular haloes with typical concentrations form discs when their central potential is not particularly steep.

Comparison to galaxies without discs
So far we have focused on the artemis galaxies that form discs (i.e.reach  co ≥ 0.5) at some snapshot.We now compare these to the general properties of those which do not reach this threshold at any time.Note that only 10 artemis galaxies fail to become discs at any time, so the following analysis is based on a reasonably small sample.
In Fig. 6 we show the corotation parameter  co , virial mass  200c , circular velocity ratio and accreted stellar fraction vs lookback time   .As in Figs. 1 and 3, the coloured lines and bands correspond to the median and 16th-84th percentile ranges of the quantities as a function of   for the two samples.Galaxies with  co ≥ 0.5 in any snapshot are shown in green and those without are in purple.
The  co dependence shows the expected behaviour.The disc galaxies reach  co ∼ 0.5 by   ∼ 8 Gyr, with some decreasing below 0.5 later (these are the 'former discs').The non-disc galaxies have significantly lower values of  co , never exceeding 0.5 by construction.The virial mass behaviour is however similar between the two samples.This suggests that while the virial mass at early times determines the epoch of disc formation (see Figs. 2, 4 and 5), it does not dictate whether or not a disc forms.The same can be said of the circular velocity ratio, although the non-discs do have slightly higher values on average in most snapshots.
The most significant difference between the two samples can be seen in the accreted stellar fraction.At   ≈ 10 − 12 Gyr the median accreted fraction in non-disc galaxies increases to more than double that in those which form discs, with the 84th percentile being much higher.This period corresponds to the time at which the discs are forming (top panel and Fig. 1).This is a strong indication that the failure to form a dominant disc may be due to massive mergers at   ∼ 10 Gyr.

SUMMARY AND CONCLUSIONS
We have used the artemis simulations of galaxies in Milky Waymass haloes to investigate the spin-up of discs.We have focused on the relations between the time of disc spin-up and the mass assembly histories of parent haloes, including the presence of a merger and associated kinematic signatures similar to the Gaia Sausage-Enceladus (GSE) merger in the Milky Way.Our results and conclusions can be summarised as follows.
(i) Most galaxies with discs at  = 0 form their discs at higher metallicity than the Milky Way.artemis galaxies with a GSE-like feature form discs earlier and at lower metallicities than those without, and are closer to the track of the median   − [Fe/H] of the Milky Way (see Fig. 1).We select six early spin-up galaxies which are similar to the Milky Way (those with the highest median   at [Fe/H] = −1), five of which have a GSE-like feature.
(ii) The distribution of stars before the disc forms is irregular without a well-defined disc or flattening (see Fig. A1).There is thus no evidence in simulations for the existence of an ancient metal-poor disc before the main disc spin-up.
(iii) There is a correlation between spin-up time  spin and halo mass at a lookback time of   = 12 Gyrs: earlier spin-ups occur in galaxies with larger  200c and  max at   = 12 Gyr (see top and middle panels of Fig. 2).In particular, the six early spin-up galaxies have the largest halo masses and  max at that epoch and experience the earliest spin-ups ( spin > 8 Gyr).
(iv) The spin-up time also anti-correlates with the fraction of accreted stars at  = 0. Galaxies with early spin-ups and discs tend to have smaller accreted fractions than those with later spin-ups (bottom panel of Fig. 2 and Fig. 3).We estimate the accreted stellar mass fraction in the Milky Way, and find that only two artemis galaxies have comparable fractions.Both of these have Milky Way-like spin-ups (at early times and low metallicities) and are both massive at early times.Galaxies with a GSE-like feature also tend to have lower accreted fractions, supporting the conclusions of Dillamore et al. ( 2023) that these undergo fewer major mergers than those without.
(v) We show that discs in artemis galaxies form when their haloes reach masses of  200c ≈ (6 ± 3) × 10 11  ⊙ (top panel of Fig. 4), similar to the mass at which galaxies are expected to form hot gaseous haloes and transition from the cold-to hot-mode accretion regime.We also show that the mass distribution becomes concentrated after the disc forms (see bottom panel of Fig. 4 and associated discussion in Section 4.2), suggesting that it is not the cause of disc formation.
(vi) While the virial mass is related to the time at which the disc forms, it does not exclusively determine whether or not disc formation happens at all.The galaxies which never form discs have similar mass growth profiles to those which do, but a significantly larger proportion of their stellar populations are accreted, particularly at early times (  ∼ 10 Gyr).This suggests that the absence of dominant disc formation may be linked to massive mergers occurring at these times.
It is clear that the Milky Way experienced mass assembly and disc formation earlier than average for haloes of its mass.Our results show that the accretion histories of Milky Way analogues are closely linked to the formation of their discs.

APPENDIX A: STAR FORMATION RATE DENSITY
In Fig. A1 we show the projected star formation rate density in each of the 18 present-day disc galaxies, from   = 12.4 to 0 Gyr.Each row corresponds to a different galaxy, labelled on the right-hand side.
The -axis corresponds to the angular momentum of the gas within  = 10 kpc in each snapshot, with the  unit vector from the previous snapshot marked with a red arrow.The galaxies are ordered by  spin , with the spin-up (marked with a red border) becoming earlier moving down the rows.The star formation is initially clumpy and irregular, with the angular momentum direction of the gas changing dramatically between subsequent snapshots.The stellar discs (parallel to the -axis) can then be seen forming in the few snapshots prior to the spin-up time, after which star formation usually takes place only close to this plane.The relation between early-time mass and spin-up time shown in Fig. 2 can also be discerned, with rates of star formation in the first few snapshots being visibly lower in the galaxies with the latest spin-ups (top few rows).
Note that the presence of a disc (i.e. co > 0.5) does not necessarily imply that star formation is occurring in a disc-like configuration.For example, the star formation in G26 and G32 at   = 0 is more dispersed.Conversely, star formation in a disc does not necessarily imply that  co > 0.5 (e.g.G24 and G27 before spin-up).In both scenarios this may be a reflection of the fact that  co describes the overall state of all stars, whereas Fig. A1 only shows where star formation is actively ongoing.A disc may therefore be present but not star forming (e.g.G26 and G32), or actively forming stars but not yet dominant (e.g.G24 and G27).We also find in a few cases (including G24 and G27) that  co approaches close to 0.5 a few Gyr before it exceeds that value.Hence their late spin-up times are partly due to their discs not becoming dominant enough until some time after their initial formation.

Figure 2 .
Figure 2. Top panel: virial mass  200 at a lookback time of   = 12 Gyr against spin-up time  spin for all haloes with  co ≥ 0.5 at the present-day (circles).Here we also show galaxies with  co ≥ 0.5 at earlier snapshots only, but not at the present-day ('former discs'; crosses).Red (blue) points indicate haloes in the (non-)GSE samples, and the early spin-up galaxies selected from Fig.1are marked with black rings.Middle panel: as above, but showing the maximum circular velocity  max (at   = 12 Gyr) against  spin .In both cases there is a correlation with spin-up time, with earlier spin-ups occurring in galaxies with higher masses and circular velocities at   = 12 Gyr.Bottom panel: fraction of accreted stars within  = 30 kpc at the present-day against spin-up time.An estimate and its uncertainty for the Milky Way is shown with a black line and grey band.Disc galaxies with earlier spin-ups tend to have lower accreted stellar fractions, while the former discs (crosses) have much larger proportions of accreted stars.

Figure 3 .
Figure 3. Accreted fraction of stars within  = 30 kpc as a function of lookback time.In each snapshot all accreted stars present in the host galaxy at that time (within 30 kpc) are included in the calculations.The lines and bands have the same meanings as in Fig.1.At   < 11 Gyr the non-GSE galaxies have a higher median fraction of accreted stars, with a median of about 30% at   = 10 Gyr.With one exception the early spin-up galaxies generally have low accreted fractions (≲ 0.1).

Figure 4 .
Figure 4. Top panel: Virial mass  200c vs time for the 18 present-day disc galaxies (coloured lines).The spin-up times and masses at the corresponding snapshots are shown by the coloured points, where the colours have the same meanings as in Fig.2.The population of former discs is also shown with the grey band, which spans between the 16th and 84th percentiles of  200c as a function of time.The panel shows that disc in the artemis galaxies form when their haloes reach mass of  200c ≈ (6 ± 3) × 10 11  ⊙ .Bottom panel: the ratio of the circular velocity  c = [  tot (<  )/ ] 0.5 at the stellar half-mass radius  eff to that at 3 eff , which we use as a measure of mass concentration and steepness of the potential.The panel shows that discs in the artemis galaxies generally form when the mass is not very centrally concentrated ( c ( eff )/ c (3 eff ) < 1), but the mass distribution becomes centrally concentrated after the disc forms.The former disc galaxies generally behave similarly to the present-day discs.

Figure 5 .
Figure5.Like Fig.4, but  200c and the circular velocity ratio are plotted as functions of  co .The left-hand column shows present-day discs, and the right column shows former discs.The spin-up threshold of  co = 0.5 is marked with a red dashed line.This confirms that spin-up occurs when the virial mass reaches the range  200c ≈ (6 ± 3) × 10 11 , whereas the circular velocity ratios span a wide range of values when  co crosses 0.5.The behaviour is generally more chaotic for the former discs, in which  co exceeds 0.5 before decreasing again.
median   as a function of age, with red (blue) indicating GSE (non-GSE) galaxies.The solid lines and bands indicate the medians and 16th-84th percentile ranges of each sample.Middle panel: as above, but as a function of [Fe/H].Data from the Milky Way is shown with the black dashed line.The dotted lines mark the individual artemis galaxies selected as 'early spin-up', those with the highest median Figure 1.Left-hand panel:  at [Fe/H] = −1.These have similar spin-up profiles to the Milky Way.Right-hand panel: as above, but median [Fe/H] as a function of age.Measurements for the Milky Way's globular clusters are shown with horizontal error bars.This demonstrates that our corrected [Fe/H] values in artemis align the [Fe/H] vs age tracks with the Milky Way's in-situ globular clusters (those with higher [Fe/H] at a given age; see Myeong et al. 2018; Massari et al. 2019).