Color-magnitude diagrams obtained with the blackbody approximation

Figure 4.3: Synthetic color-magnitude diagrams, constructed with stellar models with a chemical composition appropriate for the Small Magellanic Cloud. These have initial masses between 10 Mand 100 M. The color of each pixel represents the number of stars it contains, given that there would be 1000 stars present in the aforementioned mass range. The purple lines are the evolutionary tracks in the color magnitude diagram for a subset of evolutionary sequences. Their initial masses are indicated in purple. On the axes we show the GAIA colorG_BP−G_RP(x-axis) and magnitudeG(y-axis). In both panels we adoptα_ov=0.33 for overshooting. Left:

a semiconvection efficiency ofα_sc = 1 is assumed for all evolutionary sequences. The shown models have identical mixing parameters to those shown in the center left Hertzsprung-Russell diagram in Fig. 3.2.Right:a semiconvection efficiency ofα_sc=100 is assumed for all evolutionary sequences. These models have identical mixing parameters to those shown in the center right Hertzsprung-Russell diagram in Fig. 3.2.

4.3 Results and discussion

Figure 4.4: Same as Fig.4.3, but now with the classicalB−V color andVmagnitude on the x-axis and y-axis, respectively.

the SMC; in Chapter3, we found that efficient semiconvection is preferred because it tends to lead to stars being BSGs for a non-negligible time. This results in a seemingly better agreement of the evolutionary models with both the BSG population (observed by Blaha and Humphreys,1989; Kalari, Vink, Dufton et al.,2018) and RSG population (observed by Levesque, Massey, Olsen et al.,2006; Davies, Crowther and Beasor,2018).

We find that in this population of stars, where 10≤ M/M ≤ 100,α_ov =0.33 andα_sc =100, the blue-to-red supergiant ratio is about 1:2.5. This seems to be at odds with the number distributions we showed of BSGs and RSGs in Chapter3, where we found that in the case ofα_ov=0.33 andα_sc=100 this ratio is close to unity. The explanation for this apparent discrepancy is that there, we only considered a subset of this population with 4.70≤ log

L/L

≤ 6.05 (we did this to be consistent with Davies, Crowther and Beasor (2018), who considered the same luminosity range). Importantly, this excluded stars with initial masses near 10 M, which contribute heavily in population statistics because they are favored by the initial mass function and they live for a long time.

The difference in evolution between theα_sc=1 andα_sc =100 populations also shows in the CMDs we present in this section. Below we discuss these CMDs individually.

GAIA: In the left panel of Fig.4.3, which shows the GAIA colors and magnitudes of theα_sc =1 population, stars are expected to be observed almost exclusively in two narrow bands: the main sequence at G_BP−G_RP ≈ −0.5 and the red giant branch atG_BP−G_RP ≈ 1.5. In the right panel of Fig.4.3 (α_sc=100), there is also a population of helium burning BSGs which is close to the main sequence, but could ideally be observed as a seperate population.

In both panels, the evolutionary tracks do not cover the mid-bottom and bottom right of the plot. The reason for this is that we only show stars of M>10 M, which all have a relatively high temperature at the beginning of their hydrogen-burning lifetime (T_eff &25 kK, see Chapter3) – compared to when they are more evolved. They emit most of their radiation in the ultraviolet range of the spectrum, which does not pass through the GAIA filters. This is illustrated in Fig.4.1. Thus, the stars begin their evolution with highG-band magnitudes (i.e., they are dim in theGband) and as they evolve and cool down, they move towards lowerG-band magnitudes. Once they reach very low temperatures, theG-band magnitude can increase again because the spectrum shifts towards the infrared, which is only marginally transmitted by

Figure 4.5: Same as Fig.4.3, but now with the classicalU−Bcolor andBmagnitude on the x-axis and y-axis, respectively.

this filter.

When CMDs are constructed using other filters our evolutionary models show, in general, similar behaviour. We discuss the similarities and differences below for the CMDs constructed using classical U BVand Hubble filters.

B-V: In the right panel of Fig.4.4, an identifiable BSG population is also visible. However, theB−V color at the hot end is somewhat less sensitive to the effecive temperature of the star (when compared to theG_BP−G_RPcolor). The main sequence and BSG populations are closer to each other and merge for the least luminous BSGs.

U-B: TheU−BCMD looks similar to theB−VCMD, although the color is slightly less sensitive to changes in the temperature (for the black body approximation, at least). However, there seem to be no advantage compared to using theB−Vcolor because theU−Bcolor can be expected to have a larger error. The reason for this is that extinction is stronger at shorter wavelengths (Gordon, Clayton, Misselt et al.,2003).

U-V: Fig.4.6that theU−V color is more sensitive to changes in effective temperature than theB−V andU−Bcolors, which both span about 1.5 magnitude. This is not surprising, as this color is simply the sum of the two other colors: (U−B)+(B−V)=U−V. As such, it spans around three magnitudes, which makes it more easy to distinguish between the main sequence and BSG populations.

F336W - F814W: Because theF336W andF814Wfilters are relatively narrow and far apart, this CMD with HST colors and magnitudes (Fig.4.7) has the largest spread in color. This is advantageous in case precise measurements (and in a large enough quantity) could be obtained. However, in theF336 filter the magnitudes obtained from the black body approximation and the synthetic spectra show the largest discrepancies, because its entire wavelength range is in the Balmer jump (Fig.4.2and Fig.4.1).

Unfortunately, we do not have synthetic colors and magnitudes of these HST filters, so we do not discuss them later on.

4.3 Results and discussion

Figure 4.6: Same as Fig.4.3, but now with the classicalU−V color andVmagnitude on the x-axis and y-axis, respectively.

Figure 4.7: Same as Fig.4.3, but now with the Hubble Space TelescopeF336W−F814W color andF814W magnitude on the x-axis and y-axis, respectively.

Figure 4.8: The relation between color and effective temperature, calculated using the synthetic atmosphere models.

We show this for the GAIA colorG_BP−G_RPand for the possible combinations of the classicalU BVfilters. The color indicates the logarithm of a model’s surface gravity in units of cm s⁻². For reference, we also show (with black lines) the relation between effective temperature and color when the black body approximation is used.