# Is the ratio $L_B / L_{H\alpha}$ important to determine star formation rates?

Could someone please tell me if the ratio $$\frac{L_B}{L_{H\alpha}}$$

is important in determining star formation rates?

Additionally, could someone please explain the implication of the ratio to me or direct me to a source?

• You should give more details like what are the terms in this ratio to make your question clearer.
– MBR
Dec 14 '17 at 8:53
• Is $L_B$ the $B$ band luminosity? If so, the ratio is a color. That doesn't really constrain the SFR (although larger SFRs generally lead to bluer colors). But your denominator can be used alone, through the Kennicutt (1998) relation: $\mathrm{SFR} = 7.9\times10^{-42} L_{\mathrm{H}\alpha}$.
– pela
Dec 14 '17 at 12:09

I assume that $$L$$ stands for lumniosity, i.e. energy emitted per time interval, and the index is refering to the respective band:

• $$L_{H \alpha}$$ is the lumniosity of the visible spectral line in the Balmer series with $$656.28 {\rm nm}$$ wavelength
• $$L_B$$ might be the lumniosity for B band, i.e. for radio frequencies between $$250\ldots 500 {\rm MHz}$$, or for blue light of wavelength $$445 {\rm nm}$$ with FWHM of $$94 {\rm nm}$$, as defined by the photometric system - which is the more proable assumption.

There are some star-formation-rate indicators based on lumniosity, but those seem to be based on a single band:

[...] with constant star formation of 100 Myr, the non-ionising UV $$(0.0912 \mu{\rm m} < \lambda < 0.3 \mu {\rm m})$$ stellar continium can be converted to a SFR:

$$SFR(UV) = 3.0 \cdot 10^{-47} \lambda \, L(\lambda)$$ with SFR(UV) in $$M_\odot {\rm yr}^{-1}$$, $$\lambda$$ in $$\overset{\circ}{A}$$, and $$L(\lambda)$$ in erg/s.

As @pela already mentioned in 2017, there is some relationship between star formation rate (SFR) and lumniosity of the $${\rm H \alpha}$$ line alone, here cited from Daniela Calzetti's web paper, which essentially is arXiv:1208.2997 