adsabs/FOCAL huggingface dataset:
Next, we try to convert the Galactic SN rate into a constraint on the Galactic SFR. According to Horiuchi et al. (2011) and Botticella et al. (2012), a cosmological SN rate is linked to the cosmological SFR as
3



RSN(z)=∫mlSNmuSNϕIMF(m)dm∫mlmumϕIMF(m)dmψSFR(z)≡kSNψSFR(z),

where 



RSN(z)

 is the SN rate, ψ
SFR(z) is the SFR as a function of redshift (z), ϕ
IMF is the initial mass function (IMF), m is the mass of a star, (m

l
–m

u
) is the mass range of IMF, (



mlSN

–



muSN

) is the mass range of SN stars, and 



kSN

 is the scaling factor between 



RSN

 and ψ
SFR by the number fraction of stars per unit mass. We apply this relationship for the Galactic SN rate and averaged Galactic SFR; therefore, 



RSNgal=kSNψSFRgal

. We show the constraint on 



ψSFRgal

 and 



kSN

 with 90% CL as shown in Figure 4. The yellow vertical band is an expected range of 



kSN

 = (0.0068–0.0088)



M⊙−1

 assuming the (modified) Salpeter-type IMF (Salpeter 1955; Horiuchi et al. 2011; Madau & Dickinson 2014), which contains uncertainties from astronomical observations and models. The lowest value of 



kSN

 is calculated from the IMF with a power index of the mass γ = −2.35 in the mass range of 0.1–100 M
⊙. On the other hand, the highest value of 



kSN

 is obtained by combining the IMF with γ = −1.5 in the mass range of 0.1–0.5 M
⊙ and the one with γ = −2.35 in the mass range of 0.5–100 M
⊙. In either case, the mass range of SN stars is set in 8–40 M
⊙. The colored horizontal lines and bands correspond to an allowed 



ψSFRgal

 range reproduced from the astronomical observation to be (1–2) M
⊙ yr−1 (Murray & Rahman 2009; Robitaille & Whitney 2010; Chomiuk & Povich 2011; Davies et al. 2011; Licquia & Newman 2015). Our result thus provides the upper limit on the SFR as 



ψSFRgal

  (17.5–22.7) M
⊙ yr−1 with 90% CL assuming the Salpeter-type IMF within our Galaxy. This result disfavors a large SFR in our Galaxy and is consistent with the constraints from the astronomical observations.
Citation: Salpeter 1955
Citation function: Uses