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?

  • 2
    $\begingroup$ You should give more details like what are the terms in this ratio to make your question clearer. $\endgroup$
    – MBR
    Dec 14 '17 at 8:53
  • 1
    $\begingroup$ 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: $\mathrm{SFR} = 7.9\times10^{-42} L_{\mathrm{H}\alpha}$. $\endgroup$
    – 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

Snapshot of above mentioned website


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