MEASURING THE TYPE IA DELAY-TIME DISTRIBUTION WITH GALACTIC ARCHAEOLOGY
3.3 The Type Ia DTD in dSphs
3.3.2 Sculptor dSph: A proof-of-concept
As a test case, I consider Sculptor dSph. One of the earliest “classical” dwarf galaxies to be identified (Shapley 1938), this spheroidal galaxy has a simple SFH consisting
0 2
4 6
8 10
12 14
Lookback time (Gyr)
0.0 0.2 0.4 0.6 0.8 1.0
CumulativeSFH
Sculptor Draco Leo II
−3.0 −2.5 −2.0 −1.5 −1.0
[Fe/H]
0.0 0.2 0.4 0.6 0.8
CumulativeMDF
−3.0 −2.5 −2.0 −1.5 −1.0
[Fe/H]
0 2 4 6 8
Time(Gyr)
Figure 3.3: Properties of Sculptor, Draco, and Leo II dSphs. Top: The normalized cumulative star formation histories for the three dSphs in our sample. For Sculptor, the SFH is taken from a GCE model (de los Reyes et al. 2022); for Draco and Leo II, the SFHs are photometrically measured (Weisz et al. 2014). Middle: The normalized cumulative metallicity distribution functions of the galaxies in our sample, taken from Kirby et al. (2010). Bottom: The age-metallicity relations of the galaxies in my sample, computed by combining the SFHs and MDFs in the above panels. Light- colored lines indicate the age-metallicity relations produced when forming the last 5% of stellar mass in each galaxy.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 100
101 102 103 104 105 106
RIaSNe(Gyr−1 )
Sculptor dSph
Double-degenerate
Observed rate GCE model rate Maoz et al. (2010) Yungelson (2010) Wang & Han (2012) Ruiter et al. (2009) Mennekens et al. (2010) Bours et al. (2013) Claeys et al. (2014)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Time (Gyr)
100 101 102 103 104 105 106
RIaSNe(Gyr−1 )
Single-degenerate
Figure 3.4: The observed rate of Type Ia SNe in Sculptor dSph (dashed blue line), compared to the Type Ia rate measured by the GCE model (black dotted line) and the expected rates computed from various model DTDs (solid lines). As expected for Sculptor, RIa,obs(t)is consistent with both the GCE rate and the RIa,exp(t) corre- sponding to the Maoz et al. (2010) DTD. Shaded regions indicate the 16th and 84th percentiles computed from 105bootstrap iterations.
of one burst of star formation with a relatively short duration (e.g., Weisz et al. 2014), making it an ideal test for our DTD method. Unfortunately, because Sculptor’s SFH is extremely ancient, the most precise SFH available for Sculptor is obtained from a GCE model. This model itself requires a Type Ia DTD as an input, so I must assume a DTD in order to obtain an SFH—and an age-metallicity relation, which I derive from the SFH—and therefore to compute the observed Type Ia rateRIa,obs(t). Fortunately, in some ways this circular logic provides a useful check for our method:
since I know what DTD went into the GCE model, theRIa,exp(t)computed from this DTD should be consistent with RIa,obs(t). As an additional check, I can compare both of these rates with the Type Ia rate recorded in the GCE model.
Table 3.2: Mean absolute deviations for Type Ia rates computed from model DTDs.
Model Sculptor dSph Draco dSph Leo II dSph
Maoz et al. (2010) 15855 8460 3074
Double-degenerate models
Yungelson (2010) 67566 2017 683
Wang and Han (2012) 64902 1936 709
Ruiter et al. (2009) 67799 1904 685
Mennekens et al. (2010) 68175 2149 701
Bours et al. (2013) 68902 2250 710
Claeys et al. (2014) 69357 2027 687
Single-degenerate models
Yungelson (2010) 69508 2440 779
Wang and Han (2012) 69402 1888 700
Ruiter et al. (2009) 69508 2436 777
Mennekens et al. (2010) 62921 1996 736
Bours et al. (2013) 69044 2272 719
Claeys et al. (2014) 69093 2378 762
Note:The minimum MAD values for each galaxy are bolded.
I present the results of this test in Figure 3.4 and Table 3.2. Here, I also plot the Type Ia yield measured from a best-fit GCE model (described in Chapter 4 de los Reyes et al. 2022), in which I assumed a DTD from Maoz et al. (2010) (and adapted by Kirby et al. 2011, top curve in the top panel of Figure 3.2). The observed Type Ia rate RIa,obs(t) (dashed blue line in Figure 3.4) has a minimum delay-time of τmin = 0.2±0.1 Gyr, where the errors are intrinsic to the binning method used to compute this Type Ia rate from discrete measurements. This τmin is consistent with most of the theoretical models compiled from Maoz et al. (2014), which have minimum delay-times on the order of 0.1 Gyr. Models with later minimum delay- times—the double-degenerate model of Claeys et al. (2014), or the single-degenerate models of Wang and Han (2012), Ruiter et al. (2009), and Yungelson (2010)—are poor fits, yielding the highest mean absolute deviations from the observed rate (Table 3.2).
The shape of the observed Type Ia rate is consistent with many of the models, including both the double-degenerate and single-degenerate models. This is perhaps unsurprising, since Sculptor’s short SFH limits the time range over which I can
measure the Type Ia rates, and many of the double- and single-degenerate DTDs have similar shapes at such early times (t < 0.7 Gyr). However, the normalization of the Type Ia rates computed from the model DTDs significantly varies. Figure 3.4 clearly shows that the observed Type Ia rate is in greatest agreement with the rate expected from the Maoz et al. (2010) DTD (dark purple line in the top panel). This is further confirmed by the mean absolute deviations, which are listed in Table 3.2:
the Maoz et al. (2010) DTD produces the lowest MAD, indicating that this model is the best fit to the observations. Additionally, as expected, both the observed rate and the expected rate from the Maoz et al. (2010) DTD are qualitatively consistent with the GCE model (dotted black line).
Taken together, these suggest that our method of measuring Type Ia rates is able to self-consistently identify the correct model when the input DTD is known.