Stellar population synthesis across the Galactic disk with JJ model. Possible implications of Gaia EDR3

Kseniia Sysoliatina 1

  • 1 Astronomisches Rechen-Institut (ARI), Heidelberg

Abstract

A well-developed semi-analytic Just-Jahreiß (JJ) model has been recently calibrated against the stellar populations selected from the Gaia DR2 in the Solar neighbourhood. In this study, we present the JJ model generalised for the whole Galactic disk. The python code with tutorials is now publicly available on github, that makes the JJ model a useful tool for stellar population synthesis in a variety of tasks of Galactic archaeology.
Assuming an axisymmetric Galactic disk as a zero-approximation, the JJ model consists of the exponential thin, thick and gaseous disks, as well as spherical or flattened halo and dark matter (DM) component. The thin disk, that is assumed to evolve parallely with the thick disk, is described by input functions given in analytic form: the initial mass function (IMF), star formation rate (SFR), age-velocity dispersion relation (AVR), and age-metallicity relation (AMR). At each radial zone, the JJ model calculates a self-consistent pair of the vertical density profile and gravitation potential by iterative solving of the Poisson-Boltzmann equation. The AVR parameters are adapted at each radius in such a way, that the overall thickness of the thin disk is kept constant. However, the flaring option is also available in the model. Motivated by our Gaia DR2-based finding of the recent star formation (SF) bursts in the thin-disk SFR, we allow the thin-disk SFR to have any number of Gaussian peaks on top of its monotonously declining continuum. It is also possible to decouple the kinematics of the stellar populations associated with the SF-excess in the peaks from the kinematics of the underlying disk populations, as given by the AVR.
The generalised JJ model is complemented by a set of Padova and MIST isochrones, such that users can synthesise stellar populations and select the observable samples on the colour-magnitude diagram, as well as apply custom cuts on such quantities as ages, metallicities, logg or effective temperatures. We expect the Gaia EDR3 to be of a great value for further development of the JJ model, providing us with many samples that span over a wide range of Galactocentric distances (e.g. Red Clump, Cepheids, F stars). With the precise Gaia EDR3 parallaxes, we hope to constrain the model parameters at different radii, and therefore, to reveal the evolution history of the Galactic disk in more details than ever.

Semi-analytic Just-Jahreiß model

Context. Though many models of the Milky Way (MW) exist so far, like the Besançon model [1,2] implemented in a widely used Galaxia tool [3], our understanding of the Galaxy structure and evolution is far from being excellent. The model we present here is the semi-analytic self-consistent Just-Jahreiß model [4] (JJ model hereafter), which concentrates on the structure of the thin disk. 

JJ model includes all key MW components: 

  • Disk (thin and thick)
  • Gas (molecular and atomic)
  • Halo (stellar and DM)

The Poisson eq. in a thin-disk approximation combined with the Boltzmann eq. is iteratively solved at a fixed Galactocentric distance R to obtain a self-consistent pair of the vertical gravitational potential and the density law. 

The JJ model has a high resolution in age (25 Myr), such that the thin disk is composed of a set of 520 mono-age isothermal subpopulations. 

The properties of the thin disk are described by the following analytic functions:

  • SFR (star formation rate) - power-law function with a peak at the age of ~10 Gyr and a monotonous decline up to the present day. Recently, we also introduced a possibility to add extra peaks on top of the SFR continuum, and thus, test more complex formation histories of the disk [5]. 
  • AMR (age-metallicity relation) - describes a simple enrichment law. A monotonous increase of metallicity with time is assumed. 
  • IMF (initial mass function) - a four-slope broken power-law is adopted [5,6]. 
  • AVR (age-velocity dispersion relation) - describes the dynamical heating of the disk perpendicular to the Galactic plane (power law). 

JJ model calibration. The JJ model was calibrated locally against the data from Hipparcos and the Catalog of Nearby Stars [4,6] and SDSS star counts [7]. Then the model has been compared to the TGAS-RAVE data in the Solar cylinder up to 1 kpc from the Galactic plane, and several non-negligible model-to-data discrepancies were identified [8]. Recently, the JJ model has been calibrated against the Gaia DR2 data in the Solar neighbourhood and 22 model parameters were self-consistently updated [5] (also see the poster of A. Just - "Dynamically hot recent star bursts in the Galactic disc" ). 

Towards the global MW disk model

Fig 1. The input functions. (a) The normalized SFR of the total disk (thin + thick) at the different Galactocentric distances. The peak at the oldest ages corresponds to the thick disk formation. There are two extra data-motivated peaks added to the thin-disk SFR at ages of 3 Gyt and 0.5 Gyr [5]. There is a central radius corresponding to each peak and the peak's amplitudes are distributed normally around these R (these peaks positions yet need to be calibrated). (b) Radially-dependent thin-disk AMR (colored curves) and the thick-disk AMR same for al radii (black curve). (c) AVR consistent with the assumed SFR and a constant disk thickness. Crosses correspond to the special thin-disk populations associated with the additional peaks on SFR. (d) The assumed radial density profiles of the model components.

To extend the local JJ model to other Galactocentric distances, several assumptions are made:

  • The MW disk is axisymmetric (i.e., no spiral arms and the bulge region cannot be modeled);
  • The overall radial density profiles of the MW components are known (disk and gas - exponential laws, stellar halo - power law, DM halo - cored isothermal sphere); 
  • The overall thin-disk and thick-disk thicknesses are known (constant or flaring). 

Functions SFR, AVR, and AMR are allowed to vary with Galactocentric distance (Fig 1.):

  • The thin-disk SFR parameters at each R are chosen such, that the SFR peak shifts to older ages at smaller R, which mimics the inside-out disk growth. The thick disk SFR shape is constant at all distances.
  • The AVR and thick-disk W-velocity dispersion are scaled at the different R in order to reproduce the assumed disk thickness.
  • AMR is constrained based on the observed metallicity distributions of the APOGEE Red Clump (RC) stars and age distributions predicted by the JJ model for the same data sample (the approach used in [5] for the Solar neighbourhood). The derived AMR is naturally consistent with the observed negative metallicity gradient across the disk.

Model release and role of Gaia

Fig 2. The predicted spatial distribution of the RC thin-disk stars. (a) The radial profile of the spatial number density of RC stars averaged over |z| = [0,500] pc and shown for the different age bins. (b) Same as on panel (a), but for metallicity bins. (c) The radial profiles of the RC scale heights calculated in the different age bins. (d) Same as (c), but for metallicity bins. 

Fig 3. The W-velocity distribution functions, f(|W|), averaged over z=[0,1.8] kpc. (a) The radial variation of f(|W|) of the F stars. (b) f(|W|) in the Solar neighbourhood (can be also other R) shown for the different age bins. (c) Same as on panel (b), but for metallicity bins. 


 

Implications of the global JJ model

The JJ model can be used together with the different stellar libraries (e.g. Padova or MIST), and therefore, the modeled density laws can be converted into stellar number densities. Thus, the different stellar population samples can be investigated across a wide range of Galactocentric distances: e.g. particularly suitable samples are bright RC and F stars or Cepheids, but also main sequence stars can be studied in the extended Solar neighbourhood. The high-quality data of Gaia EDR3 (and the upcoming releases) provide us with the data needed for the future calibration of the JJ model at the different R. Also, complementary to Gaia, the data from the different spectroscopic surveys such as APOGEE, GALAH, and the future survey 4MOST are of special importance for disentangling the different disk populations and for revealing the disk evolution history. 

The new global JJ model can predict many different quantities.

  • For the different stellar populations, the following quantities can be predicted:
    • Vertical and radial density profiles (also in age and metallicity bins);
    • W-velocity distribution functions (in R, z, age, and metallicity bins);
    • Age and metallicity distributions (also in R and z bins);
    • Hess diagrams (in the local cylinder, local sphere, R-phi-z volume; more options can be added...).
  • The MW rotation curve. 

Where we stand:

The new JJ model will be presented in our next paper (Sysoliatina and Just in prep.), and the python package jjmodel will become public on Github. 

 

 

References

[1] Robin A. C., Reylé C., Derrière S., Picaud S., 2003, A&A, 409, 523

[2] Czekaj M. A., Robin A. C., Figueras F., Luri X., Haywood M., 2014, A&A, 564, A102

[3] Sharma S., Bland-Hawthorn J., Johnston K. V., Binney J., 2011, Galaxia: A Code to Generate a Synthetic Survey of the Milky Way, Astrophysics Source Code Library

[4] Just A., Jahreiß H., 2010, MNRAS, 402, 461

[5] K. Sysoliatina and A. Just., 2021, A&A, 647:A39 

[6] J. Rybizki and A. Just., 2015, MNRAS, 447:3880–3891

[7] Just A., Gao S., Vidrih S., 2011, MNRAS, 411, 2586

[8] Sysoliatina et al., Just A., Koutsouridou I., 2018,
A&A, 620, A71

 

Related poster:

A.Just - Dynamically hot recent star bursts in the Galactic disc