<p>I assume that <span class="math-container">$L$</span> stands for <a href="https://en.wikipedia.org/wiki/Luminosity" rel="nofollow noreferrer">lumniosity</a>, i.e. energy emitted per time interval, and the index is refering to the respective band:</p>
<ul>
<li><span class="math-container">$L_{H \alpha}$</span> is the lumniosity of the visible spectral line in the Balmer series with <span class="math-container">$656.28 {\rm nm}$</span> wavelength</li>
<li><span class="math-container">$L_B$</span> might be the lumniosity for <a href="https://en.wikipedia.org/wiki/B_band_(NATO)" rel="nofollow noreferrer">B band</a>, i.e. for radio frequencies between <span class="math-container">$250\ldots 500 {\rm MHz}$</span>, or for blue light of wavelength <span class="math-container">$445 {\rm nm}$</span> with <a href="https://en.wikipedia.org/wiki/Full_width_at_half_maximum" rel="nofollow noreferrer">FWHM</a> of <span class="math-container">$94 {\rm nm}$</span>, as defined by the <a href="https://en.wikipedia.org/wiki/Photometric_system" rel="nofollow noreferrer">photometric system</a> - which is the more proable assumption.</li>
</ul>
<p>There are some <a href="https://ned.ipac.caltech.edu/level5/Sept12/Calzetti/Calzetti1_2.html" rel="nofollow noreferrer">star-formation-rate indicators based on lumniosity</a>, but those seem to be based on a single band:</p>
<blockquote>
<p>[...] with constant star formation of 100 Myr, the non-ionising UV <span class="math-container">$(0.0912 \mu{\rm m} &lt; \lambda &lt; 0.3 \mu {\rm m})$</span> stellar continium can be converted to a SFR:</p>
<p><span class="math-container">$$ SFR(UV) = 3.0 \cdot 10^{-47} \lambda \, L(\lambda)$$</span>
with SFR(UV) in <span class="math-container">$M_\odot {\rm yr}^{-1}$</span>, <span class="math-container">$\lambda$</span> in <span class="math-container">$\overset{\circ}{A}$</span>, and <span class="math-container">$L(\lambda)$</span> in erg/s.</p>
</blockquote>
<p>As @pela already mentioned in 2017, there is some relationship between star formation rate (SFR) and lumniosity of the <span class="math-container">${\rm H \alpha}$</span> line alone, here cited from <a href="https://ned.ipac.caltech.edu/level5/Sept12/Calzetti/Calzetti1_2.html" rel="nofollow noreferrer">Daniela Calzetti's web paper</a>, which essentially is <a href="https://arxiv.org/abs/1208.2997" rel="nofollow noreferrer">arXiv:1208.2997</a></p>
<p><a href="https://i.sstatic.net/hHCgB.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/hHCgB.png" alt="Snapshot of above mentioned website" /></a></p>

CC BY-SA 4.0
2021-06-20T21:44:46.950Z
2021-06-20T22:03:57.867Z
2021-06-20T22:03:57.867Z
B--rian
<p>Could someone please tell me if the ratio <span class="math-container">$$\frac{L_B}{L_{H\alpha}}$$</span></p>
<p>is important in determining star formation rates?</p>
<p>Additionally, could someone please explain the implication of the ratio to me or direct me to a source?</p>

CC BY-SA 3.0
2017-12-14T08:53:38.423Z
You should give more details like what are the terms in this ratio to make your question clearer.
MBR
CC BY-SA 3.0
2017-12-14T12:09:49.687Z
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)](http://adsabs.harvard.edu/abs/1998ARA%26A..36..189K) relation: $\mathrm{SFR} = 7.9\times10^{-42} L_{\mathrm{H}\alpha}$.
pela
<star-formation><definition>
Is the ratio $L_B / L_{H\alpha}$ important to determine star formation rates?
Constantine 
# Is the ratio $L_B / L_{H\alpha}$ important to determine star formation rates?

(Asked by: username_0 on 2017-12-14)

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?

**Tags:** star-formation, definition

> **Comments:**
> **username_1**: You should give more details like what are the terms in this ratio to make your question clearer.  
> **username_2**: 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)](http://adsabs.harvard.edu/abs/1998ARA%26A..36..189K) relation: $\mathrm{SFR} = 7.9\times10^{-42} L_{\mathrm{H}\alpha}$.  

---

## 1 answers

### Answer by username_3 on 2021-06-20. Score: 1

I assume that $L$ stands for [lumniosity](https://en.wikipedia.org/wiki/Luminosity), 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](https://en.wikipedia.org/wiki/B_band_(NATO)), i.e. for radio frequencies between $250\ldots 500 {\rm MHz}$, or for blue light of wavelength $445 {\rm nm}$ with [FWHM](https://en.wikipedia.org/wiki/Full_width_at_half_maximum) of $94 {\rm nm}$, as defined by the [photometric system](https://en.wikipedia.org/wiki/Photometric_system) - which is the more proable assumption.

There are some [star-formation-rate indicators based on lumniosity](https://ned.ipac.caltech.edu/level5/Sept12/Calzetti/Calzetti1_2.html), 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 @username_2 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](https://ned.ipac.caltech.edu/level5/Sept12/Calzetti/Calzetti1_2.html), which essentially is [arXiv:1208.2997](https://arxiv.org/abs/1208.2997)

[![Snapshot of above mentioned website](https://i.sstatic.net/hHCgB.png)](https://i.sstatic.net/hHCgB.png)


---

