Figure 3.1:
Taken from Figs.6 and 7 of Kennicutt (1998).
Left: The
-axis means the total (HI+H
) gas density and the
-axis does the global star formation rate.
Right: The
-axis means the total (HI+H
) gas density divided by the orbital time-scale.
The
-axis is the same.
![\begin{figure}
\centering\leavevmode
\epsfxsize =.45\columnwidth \epsfbox{eps...
...hfil
\epsfxsize =.45\columnwidth \epsfbox{eps/Kennicutt98-2.ps}
\end{figure}](img796.png) |
The star formation rate is estimated by the intensity of H
emission
(Kennicutt, Tamblyn, & Congdon 1994) as
![\begin{displaymath}
{\rm SFR}(M_\odot {\rm yr}^{-1})=\frac{L({\rm H}\alpha)}{1.26\times 10^{41}{\rm erg s^{-1}}},
\end{displaymath}](img797.png) |
(3.2) |
which is used for normal galaxies.
While in the starburst galaxies which show much larger star formation rate than the normal galaxies,
FIR luminosity seems a better indicator of star formation rate
![\begin{displaymath}
{\rm SFR}(M_\odot {\rm yr}^{-1})=\frac{L({\rm FIR})}{2.2\ti...
...rg s^{-1}}}
=\frac{L({\rm FIR})}{5.8\times 10^{9}L_\odot}.
\end{displaymath}](img798.png) |
(3.3) |
Kennicutt (1998) summarized the relation between SFRs and the surface gas densities [Fig.3.1 (left)]
for 61 normal spiral and 36 infrared-selected starburst galaxies.
As seen in Figure 3.1,
the star formation rate averaged over a galaxy (
),
which is called the global star formation rate,
is well correlated to the average gas surface density
.
He gave the power of the global Schmidt law as
.
That is,
![\begin{displaymath}
\Sigma_{\rm SFR}\simeq (1.5\pm 0.7)\times 10^{-4}\left(\fra...
...^{1.4\pm 0.15}
M_\odot {\rm yr}^{-1} {\rm k pc}^{-2}.
\end{displaymath}](img802.png) |
(3.4) |
The fact that the power is not far from 3/2 seems to be explained as follows:
Star formation rate should be proportional to the gas density (
) but it should also be inversely proportional to the
time scale of forming stars in respective gas clouds, which is essentially the free-fall time scale.
Remember the fact that the free-fall time given in equation (2.26) is proportional to
.
Therefore
![\begin{displaymath}
\rho_{\rm SFR}\propto \rho_{\rm gas}\times (G\rho_{\rm gas})^{1/2} \propto \rho_{\rm gas}^{3/2},
\end{displaymath}](img804.png) |
(3.5) |
where
and
are the volume densities of gas and star formation.
He found another correlation between a quantity of gas surface density divided by the
orbital period of galactic rotation and the star formation rate [Fig.3.1 (right)].
Although the actual slope is equal to 0.9 instead of 1,
the correlation in Fig.3.1(right) is well expressed as
![\begin{displaymath}
\Sigma_{\rm SFR} \simeq 0.017\Sigma_{\rm gas}\Omega_{\rm gas} = 0.21 \frac{\Sigma_{\rm gas}}{\tau_{\rm arm-to-arm}},
\end{displaymath}](img807.png) |
(3.6) |
where
represents the angular speed of galactic rotation.
This means that 21 % of the gas mass is processed to form stars per orbit.
These two correlations [eqs. (3.4) and (3.6)]
implicitly ask another relation of
.
Kohji Tomisaka
2012-10-03