3 Warm molecular hydrogen emission: Excitation temperatures and masses

Using the pure rotational H₂ lines we can probe the physical conditions of the warm molecular hydrogen in our sample of Starburst and Seyfert galaxies. As we discussed in Sect. 1, the pure rotational lines originate from the warm (T< 2000 K) gas. In what follows we derive excitation temperatures for the "warm'' molecular hydrogen gas as well as masses and compare them to the total masses of the galaxies, as probed by observations of the various transitions of the CO molecule. We also compare and discuss the global properties of the "warm'' gas in starbursts and Seyferts.

3.1 Excitation temperatures and masses

The excitation diagrams in Figs. 3 and 4 show a plot of the natural logarithm of the column density divided by the statistical weight in the upper level of each transition against the energy level. The column density follows from the Boltzmann equation,

$$\frac{N_{i}}{N} = \frac{g(i)}{Z(T_{\rm ex})} \times \exp\left(-\frac{T_{i}}{T_{\rm ex}}\right)$$ (1)

where N_i is the column density of H₂ in the ith state, g(i) and T_i are the statistical weight and energy level of that state, N is the total column density of H₂, $T_{\rm ex}$ is the excitation temperature, and $Z(T_{\rm ex})$ is the partition function at $T_{\rm ex}$. N_i is calculated from the observed quantities according to:

$$N_{i} = \frac{{\rm flux}(i)}{A(i)\times h \times \nu(i)} \times \frac{4\pi}{\rm beam}$$ (2)

where flux(i) is the flux of a line in the ith state, A(i) is the A-coefficient of that transition, $\nu(i)$ is the frequency of the transition, h is Planck's constant, and beam is the solid angle of the beam size. In Figs. 3 and 4 we plot the natural logarithm of Eq. (1).

Figure 3: Excitation diagrams for the starbursts.

Figure 4: Excitation diagrams for the Seyferts.

For the excitation diagrams we used extinction-corrected line fluxes. We estimated the extinction for each line flux using the A_V values listed in Tables 1 and 2. For $\lambda<8$ $\mu$m we used $A(\lambda)\propto \lambda^{(-1.75)}$ and for $\lambda>8~\mu$m the extinction law of Draine & Lee (1984) and Draine (1989) were used. We assumed similar obscuration of the ionized and molecular media.

   

Table 2: The Seyfert sample galaxies.

Galaxy Name	D	A V	Spec. type	comments
	Mpc	[mag]
NGC 1068	14	81	Sy2	SAb
NGC 1275	70	22	Sy2	cD, pec.
NGC 1365	22.3	2.52	Sy1.8	SBb
NGC 4151	20	31	Sy1.5	SABab
Cen A	4	303	Radio	SO pec.
NGC 5506	23	83	Sy1.9	Sa pec.
Circinus	3	203	Sy2	SAb
NGC 7582	20	183	Sy2	SBab
NGC 7469	66	201	Sy1.2	SABa

¹ A_V mixed case (from Genzel et al. 1998).
² NGC 1275: Krabbe et al. (2000); NGC 1365: Kristen et al. (1997).
³ A_V screen case (from Genzel et al. 1998).

 

 

Table 3: H₂ emission line fluxes - starbursts.

Galaxy Name	(1-0)Q(3)	S(7)	S(5)	S(3)	S(2)	S(1)	S(0)
$\lambda (\mu \rm m)$	2.42	5.51	6.91	9.67	12.27	17.03	28.22
			$\times$10-20 W cm-2
NGC 253	2.80	8.40	11.5	-	12.0	19.57	2.13
IC 342	0.39	<0.9	1.60	-	2.50	4.90	0.80
IIZw40	-	-	<0.45	-	<4.5	<0.85	-
M 82	2.65	4.80	11.50	-	12.0	15.0	7.8
NGC 3256a	0.38	-	4.70	-	2.35	11.50	<3.90
NGC 3690A	<0.3	-	1.97	-	1.8	3.7	<1.21
NGC 3690B/C	<0.4	-	1.46	-	1.92	4.11	<0.7
NGC 4038b	-	-	-	-	1.6	3.95	-
NGC 4945c	3.2	1.11	15.4		7.45	15.1	4.82
NGC 5236 (M83)	-	-	2.84	-	-	7.29	<1.04
NGC 5253	0.55	-	<0.60	-	-	0.50	-
NGC 6946d	-	-	-	-	<0.93	2.73	0.41
NGC 7552	<0.86	1.08	2.37	2.84	<1.5	5.11	<0.52
H2 line fluxes from:
a Rigopoulou et al. (1996).
b Kunze et al. (1996).
c Spoon et al. (2000).
d Valentijn et al. (1996).

   

Table 4: H₂ emission line fluxes - Seyferts.

Galaxy Name	(1-0)Q(3)	S(7)	S(5)	S(3)	S(2)	S(1)	S(0)
$\lambda (\mu \rm m)$	2.42	5.51	6.91	9.67	12.27	17.03	28.22
			$\times$10-20 W cm-2
NGC 1068a	2.296	-	6.403	5.757	-	6.502	<1.872
NGC 1275	<0.8	0.9	1.55	-	<1.0	2.06	<2.2
NGC 1365	<0.85	-	2.01	-	<3.13	5.69	<1.65
NGC 4151	-	-	1.32	-	<1.86	1.667	<1.26
CenA	0.792	3.259	4.535	5.806	5.397	8.635	2.511
NGC 5506	-	-	1.508	-	<0.859	1.185	<0.928
Circinus	-	2.72	7.97	-	2.36	13.94	1.56
NGC 7582	-	-	1.945	-	<1.289	3.116	0.764
NGC 7469	-	-	1.394	-	2.125	2.955	0.8
H2 line fluxes from: a Lutz et al. (2000).

The excitation temperature of the line-emitting gas is the reciprocal of the slope of the excitation diagram, corresponding to the kinetic temperature in local thermodynamic equilibrium (LTE). Assuming thermal emission, it is apparent that H₂ is present in a range of temperatures in all cases. The excitation temperature changes rapidly with energy level. This is of course a natural consequence of the fact that the gas is in reality consisting of various components at various temperatures. The detections of the S(1) and S(0) lines (or the upper limits of the latter whenever not detected) are used to constrain the temperature of the "warm'' line emitting gas, while the S(5) and S(7) lines are used to constrain the temperature of the somewhat "hotter" gas. In fact the S(5) and S(7) lines most likely probe the same excited gas as the near-infrared ro-vibrational lines. Therefore, the detection of the S(0) and S(1) lines is more important since we can probe the more abundant "warm'' gas. In Tables 5 and 6 (Cols. 2 and 5 respectively) we list the temperatures (for the "warm'' and the "hotter'' gas) for the starbursts and Seyferts, respectively.

We note that the derived excitation temperature is affected by the total ortho-to-para conversion rate of H₂. For the calculations above we have assumed an ortho-to-para abundance ratio of 3, the equilibrium value for temperatures $T\geq200$ K (assuming LTE conditions). Sternberg & Neufeld (1999) have measured an ortho-to-para ratio of 3 in the PDR star-forming region S140. Assuming a lower ortho-to-para conversion rate of 1 we find higher values of $T_{ \rm S(0)-S(1)}$and lower values of $T_{ \rm S(2)-S(1)}$, internally inconsistent and implying that multiple temperature components should be considered to fit the data. We believe that under the assumption of LTE conditions an ortho-to- para abundance ratio of 3 is a realistic value.

From the S(0)-S(1) detections in starbursts we derive an average temperature of $T_{\rm SB} \sim160\pm10$ K. For those starbursts for which there was no S(0) detection we used the S(1) and S(2) detections to find the range of temperatures. For the starbursts we find $150\leq T_{\rm SB}\leq330$ K. For the Seyferts, the S(0) line is detected in CenA, Circinus, NGC 7582 and NGC 7469. Based on these detections we derive an average temperature $T_{\rm Sey} \sim 150\pm12$ K. For those Seyferts with S(0) non-detections we derive limits in the range $120\leq T_{\rm Sey}\leq370$ K (using S(1) and S(2)). Although the number of S(0) detections in the Seyfert sample is slightly smaller (in the present sample the S(0) line is detected in 5/10 of the starbursts and 4/9 of the Seyferts) it is obvious that the temperatures of the "warm'' gas are, within the errors, similar in starbursts and Seyferts.

Taken at face value the similar temperatures found for starbursts and Seyferts indicate that the conditions in the gas are the same in both environments. Although this could have been the anticipated result (since we are looking at the same transitions originating in "warm'' clouds in galaxies) we caution that a number of factors may contribute to this effect: first, most of the Seyferts in our sample are "mixed'' objects that is, there is evidence for the presence of an extended starburst component (e.g. NGC 7469, NGC 7582, CenA and Circinus) whose energy output is comparable to that of the central active nucleus. Second, the large SWS apertures sample a mixture of molecular hydrogen emission from cool clouds in the extended circumnuclear regions as well as the warmer central clouds. Thus, effects of dilution of a pure AGN-related effect by the more extended starburst activity are possible. Such a behaviour has already been noted in the case of NGC 1068 (Lutz et al. 2000) where the SWS-H₂ emission traces gas originating both in the central active nucleus as well as the molecular ring which is present at larger spatial scales.

We next derive masses corresponding to the gas found at various temperatures, mostly the "warm'' gas emitting the S(0) line as well as the "hotter'' higher excitation gas in which the S(7) line originates. The various masses are derived based on the following method: the column density (from Eq. (1)) is multiplied by the physical area of the object corresponding to the aperture. For aperture sizes we use the values quoted in Sect. 2 depending on the transition (either S(0) or S(7)). The "warm'' molecular masses were derived using the S(0) line (column density and temperature). In the cases of undetected S(0) lines we have used the S(1) line (column density) and the S(1)-S(2) temperature to derive the masses. The "hotter'' gas masses are derived using the S(7) detections. The "warm'' gas masses (denoted as M ₁) and the "hotter'' gas masses (denoted as M ₂) are listed in Tables 5 and 6 (Cols. 3 and 6) for starbursts and AGN, respectively.