Properties of White Dwarfs in the JJ model based on Gaia EDR3

Akash Vani 1 , Andreas Just 1 , Kseniia  Sysoliatina 1

  • 1 Astronomisches Rechen-Institut, ZAH, Heidelberg University, Heidelberg

Abstract

The Just-Jahreiß (JJ) model is a semi-analytic evolutionary model of the Milky Way (MW) Galactic disk (Just & Jahreiß 2010). It has been recently updated and calibrated in the Solar neighbourhood against the Gaia DR2 stars and is applicable for a wide range of Galacto-centric distances, 4 kpc<=R<=14 kpc (Sysoliatina & Just 2021, Sysoliatina & Just 2022 in prep.). The model includes four flattened and two spheroidal components of the MW describing it as an axisymmetric and plane-symmetric system. It is based on an iterative solving of the Poisson equation, and thus, reconstructs a self-consistent pair of the overall vertical gravitational potential and density profile. The thin disk is modelled in a presence of gas, thick disk, stellar halo, and dark matter components. The model describes the evolution of the thin disk as a set of isothermal mono-age stellar population whose evolution is governed by four inputs, namely, a declining Star Formation Rate (SFR), a four-slope broken power law Initial Mass Function (IMF), a dynamical heating law described by an Age Velocity Relation (AVR) and a monotonically increasing Age Metalicty Relation (AMR). The JJ model uses the PARSEC isochrones and the AMR to populate the 3D age-metalicity-mass parameter space, until the thermally pulsing asymptotic giant branch (TP-AGB) phase. It has been demonstrated to have a good model-to-data consistency (with a ~4% discrepancy in terms of star counts) in the local 1-kpc height cylinder.

It is known that stars with initial masses lower than ~8M_sun, i.e., ~97% of the stars in our Galaxy, are destined to evolve into white dwarfs (WD). The evolution of WD can be described by its slow cooling process, due to which they act as cosmic clocks. They are used to infer the age of a wide variety of stellar populations, such as the Galactic disk and halo, and the system of globular and open clusters. Given the importance of these objects, this work deals with extending the JJ model to the WD locus. We use the Initial Final Mass Relation (IFMR) to form a bridge from the main sequence to the WD. It is known that ~80% of the WD are H-dominated (DA). Thus, we use cooling sequences for three different types of WDs; thin and thick layered H-dominated (DA) WD and non-Hydrogen dominated WD to further evolve the current population in the JJ model. We then use Gaia EDR3 data to test and calibrate it and also compare the star count against the model. In this work, we also compare different IFMRs and cooling sequences in the JJ model for the solar neighbourhood.

Keywords: Stars: white dwarfs, Galaxy: kinematics and dynamics, Galaxy: solar neighbourhood

JJ model vs GCNS

60pc sample

We found the GCNS (Smart, R. 2021) is complete until ~15 MG up to a distance of ~60 pc. Thus, we use this sub-sample for further analysis.

Similar to the CNS5, we compare the stellar content of the 60 pc GCNS sub-sample to the JJ model.

Figure 5.


(Left panel) CMD of the 60 pc GCNS sample. It includes a total of 63759 stars out of which there are 4199 WDs.


(Right panel) CMD generated by the JJ model and it contains a total of 65564 stars out of which 3810 are WDs. 

Figure 6.


(Left panel) A plot of the difference between the data and model. Unresolved binaries are seen on the upper edge of the MS branch.


(Right panel) A plot of the ratio of data and model, to highlight the inconsistencies in the model. Similar to the CNS5, on the upper edge of the MS branch we can see this as an overdensity caused by unresolved binaries. and turn off stars. SImaraly there is an overdensity of hot and bright WDs. 

We apply a cut at 15 MG and 1.5 G-RP color as per the applicability range of the MS isochrones. WD isochrones will go below 15 MG and this overdensity of old WD will be magnified.

The inconsistency between the total star count between the data and the model is less than 3 % and the inconsistency between the WD counts is around 9 %. 

The WD data-to-model consistancy is good, however the model predicts a higher number of old WDs, suggesting that the early star formation rate needs be adapted.

It is to be noted that we also apply G-RP correctoons aimed to mitigate the effects of blending and conatmination (CNS5, Golovin, A., et al. 2022 submitted).

Low mass WDs with helium core are not included and we expect to see this as a discrepancy on the CMD on the upper edge of the WD branch.

JJ model vs CNS5

25 pc sample

We compare the stellar population generated from the JJ model with the stellar content of the 5th Catalogue of Nearby Stars (CNS5) (Golovin, A., et al. 2022, submitted). CNS5 is a volume-limited catalogue of all stars (including WDs and brown dwarfs) within 25 pc. It also includes a complete sample of 260 WDs.

Figure 3.


(Left panel) CMD of the CNS5 sample includes a total of 4738 stars out of which there are 260 WDs.


(Right panel) The CMD generated by the JJ model contains a total of 4780 stars out of which 277 are WDs. 

Figure 4.


(Left panel) A plot of the difference between the data and model. Unresolved binaries in the data are seen as artifacts along the upper edge of the MS.


(Right panel) A plot of the ratio of data and model. This plot focuses on the inconsistencies of the model. The color coding represents where the data is more than the model. On the upper edge of the MS branch we can see this as an overdensity caused by unresolved binaries. and turn off stars. SImaraly there is an overdensity of hot and bright WDs. 

We apply a cut at 15 MG and 1.5 G-RP color as per the applicability range of the MS isochrones.

We see a good model-to-data consistency after including the WDs. The inconsistency between the total star counts is about 1 %, while the inconsistency between the number of WDs is around 9 %. 

The model predicts a higher number of WDs and most of them are old, this could be a sign that the early star formation rate needs to be adapted.

It is to be noted that we also apply G-RP correctoons aimed to mitigate the effects of blending and conatmination (CNS5, Golovin, A., et al. 2022 submitted).

Future goals, stay tuned!

  • Currently, we include only carbon-oxygen core WDs. The next step is to include oxygen neon core WDs to show the development of the Q-branch. 

  • The next planned step is to test the JJ model for different WD cooling models which are available in the literature and also different initial final mass relations and for its metallicity dependence.

  • The JJ model does not currently include binaries and binary evolution, including this would improve the data-to-model consistency.

References

JJ model

 

Isochrones

 

Initial final mass relation

 

Data

 

Related ePoster on the JJ model at EAS 22

 

Hello, I am Akash, a master's student at University of Heidelberg, Germany. You can find more about me on my website (here) or on LinkedIn (here).

Feel free to contact me by email: akash.vani@stud.uni-heidelberg.de

MS and WD isochrones

Figure 2. Animation of the PARSEC isochrones for the MS stars and BaSTI isochrones for carbon-oxygen DA WDs. Both isochrones are calculated for solar metallicity. The plot also shows the colour magnitude diagram of the GCNS sample for stars within 60 pc in Gaia bands (black points). The blue and red colour coding shows the mass of the object. The animation is constructed with an age step of 100 Myr.

To include WDs we use Cummings J.D., et al. (2018) initial final mass relation bridge the MS and the WDs. We then use carbon oxygen H atmosphere (DA) and He atmosphere (DB) WD isochrones from BaSTI (Salaris M., et al 2022).

We use solar metallicity BaSTI DA WD isochrones from 80 Myr to 12.7 Gyr for an age step of 50 Myr. Similarly, DB WD isochrones from 80 Myr to 5.7 Gyr (This is due to the physical limitation in the BaSTI code). For simplification, assume the DA to DB ratio to be fixed at 80 % to 20 % for all temperature ranges.

 

Introduction and background

Figure 1. Schematic view of the different components of the Milky Way included in the JJ model.

JJ model framework

The Just-Jahreiß (JJ) model (Just, A. and Jahreiß, H. 2010) is a semi-analytic model of the Milky Way (MW) Galactic disc and is a flexible tool for stellar population synthesis with a fine age resolution of 25 Myr. It is based on an iterative solving approach of the combined Poisson-Boltzmann equation.

It is based on the following assumptions:

  • MW disk is in a steady-state
  • It is axisymmetric and plane-symmetric
  • It assumes a flattened disc
  • No explicit radial migration
  • It consists of isothermal sub-populations

Due to these assumptions, it is not applicable to the bulge, O and B stellar population and needs to be averaged over large volumes.

For more details on the JJ model, refer Sysoliatina, K. ePoster

Stellar population synthesis

In the JJ model, we convert the density profiles to mock samples using isochrones for a wide range of metallicities (-2.59<[Fe/H]<0.47). We use PARSEC isochrones (Bressan, A., et al. 2012) for main sequence (MS) stars and also offer MIST (Dotter, A. 2016) and BaSTI (Hidalgo, S. L., et. al. 2018) MS isochrones as complementary sets. We then use it to populate a 3D age-metallicity-mass parameter space and apply an IMF (Rybizki, J. & Just, A. 2015) to get the present day number density.

As per the latest calibration paper (Sysoliatina, K. & Just, A. 2021, and Sysoliatina, K., & Just, A., 2022 submitted) using Gaia DR2, we find a good data-to-model consistency (with a ~4 % discrepancy in the total star counts) for a 1 kpc height cylinder while a ~0.1 % discrepancy against the CNS5 sample, a 25pc volume-limited sample (Golovin, A., et al., 2022, submitted). 

Why white dwarfs ?

All stars with initial masses lower than ~8 M☉, i.e. ~97 % of the stars in our Galaxy, are destined to evolve into white dwarfs (WD). These stellar remnants have no appreciable sources of nuclear energy. Thus, they will slowly cool and radiate the stored energy and cool over time.

WDs are also used to infer the ages of different stellar populations and the star formation rate. However, the stellar libraries that are mentioned above, do not include the evolution of WDs.