ON THE FORMATION OF GALACTIC THICK DISKS

Similarly to Martig et al. (2014a), we decomposed the stellar disks into mono-age populations, i.e., narrow bins of age, where we used Δage = 1 Gyr. It was found that single exponentials provided good fits to the column density in the vertical direction for all age bins and both Model1 and Model2, in agreement with Martig et al. (2014a). Assuming that chemistry can be a proxy for age, this is also consistent with studies of mono-abundance populations in the Milky Way (Bovy et al. 2012). The top panel of Figure 1 shows single exponential fits for a typical mono-age population of Model1, in eight radial bins in the range of 1 < r < 5 disk scale-lengths, h_d. Radial bins of width 0.6h_d were used. It can be seen that the fits are very good for all radii. In contrast, the bottom panel of Figure 1 shows that a sum of two exponentials is required for a proper fit when considering the total stellar population.

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It is clear already from the top panel of Figure 1 that significant flaring exists for the particular mono-age population shown (i.e., the vertical density profile flattens with increasing radius). However, only milder variations with radius are seen for the total population when decomposed into thin and thick disks (Figure 1, bottom panel).

In the top row of Figure 2 we plot the scale-height variation with galactocentric radius, r, in the region of 1–5 disk scale-lengths, h_d, for both Model1 (left panel) and Model2 (right panel). Forty overlapping mono-age populations of width 1 Gyr are shown, covering the age range in each disk, as indicated in the color bar on the right of each panel. Both the radius and scale-height, h_z, are in units of h_d. It can be seen that, indeed, for both models significant flaring is present, which increases for older coeval populations. For Model1 the increase in scale-height with radius for stars of age ∼8 Gyr is about a factor of four in four scale-lengths. The flaring decreases by about a factor of two for stars with age <2 Gyr. Even more significant flaring is seen for Model2.

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In contrast to the flaring found for all mono-age populations, the thin and thick disk decomposition of the total stellar population including all ages results in no apparent flaring. This is shown by the triangle and square symbols overlaid in the top row of Figure 2.

We discuss the interpretation and implications of this interesting result in the following sections.

What is the reason for the flaring of mono-age disks? In numerical simulations flaring is expected to result from a number of mechanisms related to galactic evolution in a cosmological context (e.g., Kazantzidis et al. 2008; Villalobos & Helmi 2008; Bournaud et al. 2009; Aumer & White 2013). Even in the absence of environmental effects, flaring is unavoidable due to secular evolution alone (radial migration caused by spirals and/or a central bar; Minchev et al. 2012). It should be stressed here that while migration flares disks in the lack of external perturbations, during satellite–disk interactions it works against disk flaring (Minchev et al. 2014b). Yet, this is not sufficient to completely suppress the flaring induced by orbiting satellites, as evident from the top row of Figure 2. This suggests that external effects are much more important for the disk flaring we see in the simulations. Because the mass and intensity of orbiting satellites generally decreases with decreasing redshift, so does the flaring induced. It can be expected that at a certain time secular evolution takes over the effect of external perturbations.³

Resolution and sub-grid models for gas physics may set an unrealistically high lower limit for the vertical velocity dispersion of young stars (e.g., House et al. 2011). The fact that the youngest populations in our simulations do not flare (dark blue curves in top panels of Figure 2) seems to indicate that numerical issues are not important for our result (see also Martig et al. 2014b; Section 5).

What is the reason for the lack of flaring in the total disk population? In an inside-out formation scenario, the outer disk edge (where flaring is induced) moves progressively from smaller to larger radii because of the continuous formation of new stars in disk subpopulations of increasing scale-length. At the same time the frequency and masses of perturbing satellites decrease. Because of the inside-out disk growth, which results in more centrally concentrated older samples (see Figure 2, middle row), the younger the stellar population, the farther out it dominates in terms of stellar mass. Therefore, the thickened disk component results from the imbedded flares of different coeval populations, as seen in the top row of Figure 2.

From the above discussion, it can easily be seen that inside-out disk growth would always have the effect of suppressing disk flaring in the total stellar population, if not completely removing it. We produced the equivalents of Figure 2 for other disks from the two simulation suites considered here. The flaring was always strongly reduced when the total population was considered, suggesting that our results are generic.

From the top panels of Figure 2 it can be expected that morphologically defined thick disks, as in observations of edge-on galaxies, will show a decrease in age with increasing disk radius. To quantify this, in the bottom row of Figure 2 we show the mean age variation with radius for stellar samples at different distances from the disk midplane, as indicated by the color bar on the right. Slices in $|z|$ have the thickness ${\Delta }|z|=0.1{{h}_{d}}.$

We also plot the mean age of samples close to (triangles) and high above (squares) the disk midplane, to be associated with thin and thick disks defined morphologically. The two vertical ranges considered, $|z|/{{h}_{d}}\lt 0.1$ and $0.3\lt |z|/{{h}_{d}}\lt 1.0$, for the Milky Way would correspond to $|z|\lt 0.3$ kpc and $0.9\lt |z|\lt 3.0$ kpc, using a disk scale-length h_d = 3.0 kpc.

A decrease of age with radius is found for the above morphologically defined thin disk in both models. However, a significant negative age gradient is also seen in the morphological thick disks. Over the radial extent of four scale-lengths shown in Figure 2, we find a drop in mean age of ∼3 and ∼4.5 Gyr for the thick disks of Model1 and Model2, respectively.

As discussed above, our results suggest that even at distances high above the disk midplane, mean stellar age should decrease with galactic radius. As good age estimates for large stellar samples are currently unavailable, we can instead look at measurements of stellar [α/Fe] ratios. Because stars of different masses release chemical elements to the interstellar medium on different timescales, abundance ratios, such as [α/Fe], can be good proxies for age (e.g., Matteucci & Brocato 1990; Chiappini et al. 1997; Haywood et al. 2013).

Negative [α/Fe] gradients at large $|z|$ were reported by Boeche et al. (2013, 2014) in dwarfs and giants, respectively, studying data from the RAVE survey (Steinmetz et al. 2006). Anders et al. (2014) and Hayden et al. (2014) also showed a transition from a weakly positive (or flat) to a negative radial gradient in APOGEE [α/M] measurements, as the distance from the Milky Way disk midplane was increased. Similar inversion of [α/Fe] gradients has been also found in recent chemo-dynamical models (Minchev et al. 2014b; Rahimi et al. 2014; Miranda et al. 2015).

Flaring of mono-age disks can result also in the inversion of metallicity gradients with increasing distance from the disk midplane, as younger metal-rich stars in the outer disk can reach high vertical distances. Observationally, this inversion has been found in a number of spectroscopic Galactic surveys (e.g., SEGUE—Cheng et al. 2012b; RAVE—Boeche et al. 2013; APOGEE—Anders et al. 2014) and in simulations (Minchev et al. 2014b; Rahimi et al. 2014).

All of the above results are in agreement with the decline in age with radius found in this work.

Studying APOGEE data, Nidever et al. (2014) showed that, at $1\lt |z|\lt 2$ kpc from the disk plane, the high-[α/Fe] sequence dominates the inner disk (5 < r < 7 kpc), while in the outer disk (9 < r < 11 kpc) only the low-[α/Fe] sequence is present (see their Figure 10).

Flaring of younger stellar populations in the Milky Way have been reported in several works (e.g., Feast et al. 2014; Kalberla et al. 2014; Carraro et al. 2015).

All these results are in agreement with the idea of mono-age flaring populations suggested here, which allow chemically or age-defined thin-disk stars to reach large vertical distances in the outer disk.

We are suggesting here that inside-out disk formation inevitably gives rise to centrally concentrated older/[α/Fe]-enhanced populations, but at the same time—to comparable scale-lengths for the morphologically defined thin and thick disks. It can be seen in the middle row of Figure 2 that this expectation is borne out for both our models. While inside 3–4h_d mono-age populations become steeper with increasing age, the surface density profiles (of stars of all ages) close to (triangles) and high above (squares) the disk midplane run mostly parallel. Moreover, beyond 3–4h_d the thick disk profiles become flatter than the thin ones, i.e., extend further out.

A morphologically defined thick disk in the Milky Way with a scale-length larger than that of the thin disk has been reported by Robin et al. (1996) using a compilation of different data sets, Ojha (2001) using 2MASS data, and Jurić et al. (2008) using SDSS data. This is well in line with external observations and explained by the idea presented here, resolving the apparent disagreement with the centrally concentrated [α/Fe]-enhanced populations in the Galaxy reported by Bensby et al. (2011) and Bovy et al. (2012).