2 Results

2.1 A sample of Mkn galaxies detected in the CO line

The flux limited ( f60 < 1.95 Jy at 60 micron) sample of Mkn-IRAS galaxies contains 155 objects (Kandalyan et al. 1995). In order to investigate the gas properties of Mkn-IRAS galaxies, we have extracted from the literature all the objects detected in the ¹²CO(1-0) line (until May 2002). The total number of CO detected Mkn galaxies is 65. The galaxies Mkn 463, 551, 673 and 1027 have been detected in the CO line (Gao & Solomon 1999), but the details of the line parameters, such as the CO line intensity and line width, are not presented. For this reason, we did not include these galaxies in our statistics. The optical, FIR and HI data have been extracted from the LEDA and NED databases. Additional HI data are chosen from Martin et al. (1991) and Kandalyan et al. (1997). The environment information on galaxies are taken from Mazzarella & Balzano (1986); Mazzarella et al. (1991); Mazzarella & Boroson (1993); Keel & van Soest (1992). The radio continuum data are chosen from Bicay et al. (1995) except those for Mkn 158, 188, 331, 404, 759, 1466 (Marx et al. 1994) and Mkn 213, 286, 439 (Stine 1992). For the environment and structure of a galaxy the following abbreviations are used: p-pair of galaxies, i-isolated galaxy, ia-interactive galaxy. The notations: I-IRAM 30 m, F-FCRAO 14 m, O-Onsala 20 m, N-NRAO 12 m, NO-NRA 45 m, S-SEST 15 m for the radio telescopes are used. Table 1 presents the list of 61 galaxies and is arranged as follows:
Column 1: Markarian number of galaxy.
Column 2: Inclination angle in degrees (i).
Column 3: Angular diameter $a_{\rm o}$ in arcmin.
Column 4: Heliocentric radial velocity V, in $\mbox{km}~$s^-1.
Column 5: Logarithm of the FIR luminosity $L_{\rm fir}$, in solar units, calculated according to
$\log{L_{\rm fir}}=5.5954+2\log{D}+\log{(2.58f60+f100)}$, where f60 and f100 are the flux densities at 60 and 100 microns respectively, in Jy, and D is the distance to the galaxy in Mpc.
Column 6: Logarithm of the blue luminosity, $L_{\rm B}$, in solar units, calculated according to $\log{L_{\rm B}}=12.164+2\log{D}- 0.4B_{\rm To}$, where $B_{\rm To}$ is the total B magnitude corrected for galactic and internal absorption.
Column 7: Logarithm of the radio continuum power $P_{\rm R}$ at 6 cm, in $\mbox{W}~$Hz^-1, calculated according to
$\log{P_{\rm R}}=17.078+2\log{D}+\log{F_{\rm 6}}$, where $F_{\rm 6}$ is the flux density at 6 cm in mJy.
Column 8: Logarithm of the atomic hydrogen mass, $M_{\rm HI}$, in solar mass, calculated according to
$\log{M_{\rm HI}}=5.372+\log{I_{\rm HI}}+2\log{D}$, where $I_{\rm HI}$ is the integrated HI line intensity in $\mbox{Jy}~$km s^-1.
Column 9: Logarithm of the molecular hydrogen mass $M_{\rm H_2}$, in solar mass, which is calculated with use of the formula: $M_{\rm H_{2}}=4.78~L_{\rm CO}$, by taking the conversion factor from the CO emissivity into $\element{H}_{2}$ column density as $N_{\rm H_{2}}$/ $I_{\rm CO}=3\times10^{20}~$ $\mbox{cm}^{-2}~(\mbox{K}~\mbox{km}~\mbox{s}^{-1})^{-1}$(Sanders et al. 1991). The CO line luminosity is calculated according to formula:
$L_{\rm CO}=26.6~D^{2}(\mbox{Mpc})~\theta^{2}(\mbox{arcsec})~I_{\rm CO}$, where $\theta$ is HPBW of the radio telescope.
Column 10: Integrated CO line intensity $I_{\rm CO}$ in $\mbox{K}~$km s^-1.
Column 11: HI line width WHI, in $\mbox{km}~$s^-1, at half of the peak intensity.
Column 12: CO line width WCO, in $\mbox{km}~$s^-1, at half of the peak intensity. The line widths are corrected for the galaxy inclination angle.
Column 13: Morphological type (T) as in RC3.
Column 14: Environment and structure of the galaxy.
Column 15: Radio telescope used for the CO line observation.
Column 16: References for CO data.

 

 

Table 1: Sample of 61 Mkn galaxies.

Mkn	i	$a_{\rm o}$	V	$L_{\rm fir}$	$L_{\rm B}$	$P_{\rm R}$	$M_{\rm HI}$	$M_{\rm H2}$	$I_{\rm CO}$	WHI	WCO	T	Env	Tel	Ref
	( $\hbox{$^\circ$ }$)	( $\hbox{$^\prime$ }$)	$\mbox{km}~$s-1	$L_{\hbox{$\odot$ }}$	$L_{\hbox{$\odot$ }}$	$\mbox{W}~$Hz-1	$M_{\hbox{$\odot$ }}$	$M_{\hbox{$\odot$ }}$	$\mbox{K}~$km s-1	$\mbox{km}~$s-1	$\mbox{km}~$s-1
2	32	0.73	5476	10.66	10.29		9.45	9.39	7.5	167	106	0	p?	I	1, 2
35	47	1.35	935	9.08	9.21		8.00	7.60	1.0	96	41	3	i	F	3
52	58	2.06	2252	9.80			8.70	8.73	2.3	96	60	-1		F	3
88	0	0.19	9180	10.53	10.32	21.95	9.35	9.81	3.1	121	100	3	i	O	4
91	0	0.89	5101	10.56	10.05		9.40	9.58	6.0	201	113	3	i	O	4
133	28	1.12	2010	9.58	9.81		8.63	8.56	8.2	95	83	4		I	1, 2
158	68	1.73	2070	9.99	10.01	21.04	8.67	9.07	25.3	209	126	1	I		5
171	47	1.89	3033	11.38	10.60	22.83		9.78	60.0		150	9	ia	I	6
188	43	1.75	2404	9.98	10.20	21.41	8.91	9.16	22.8	270	240	5	I		7
201	61	1.61	2511	10.57	10.07	21.74	8.81	9.05	16.4	87	149	10		I	7
213	54	1.63	3115	10.04	10.29	21.36		9.03	10.1		311	1		I	1, 2
231	43	1.22	12300	12.10	10.98	23.70		10.42	16.0		197	5	ia	I	7
266	29	1.16	8358	11.18	10.69	22.82		10.37	4.9		400	7	ia	N	8
273	90	0.81	11274	11.87	10.87	23.30		10.44	19.8		494	4	ia	I	7
281	32	3.15	2227	9.96	10.42	21.07	8.86	9.19	6.8	305	278	3	i	F	9
286	27	0.85	7548	10.86	10.62	21.76	10.17	9.88	5.4	231	175	4	i	O	4
297	40	0.89	4701	10.64	10.38	22.36	9.47	9.26	12.5	366	180	5	ia	NO	10
311	0	0.43	9190	10.70	10.37	21.86	9.12	9.60	1.9	194	124	6	i	O	4
331	51	0.63	5351	11.11	10.07	22.19	9.93	10.06	16.1	264	281	3	ia	O	4
332	24	1.42	2662	10.04	10.30	20.78	8.81	9.25	22.7	80	64	5		I	5
353	60	0.72	4861	10.43	10.25		9.36	9.66	17.6	192	278	5	i	I	1, 2
363	59	3.82	2935	9.76			8.98	8.66	8.2	150		-2		NO	11
404		0.10	1320	9.82		21.25		8.96	11.4		280			F	3
439	12	2.09	988	9.26	9.58	20.24	7.97	9.08	22.5	62	70	1		I	12
496	90	1.37	8785	11.16		22.52	10.01	10.36	4.3	211	100	-3	ia	N	8
518	0	0.48	9506	10.85	10.69	22.36	9.75	10.05	5.0	242	199	10	i	O	4
533	24	1.13	8662	11.08	10.85	23.10	10.00	10.31	4.0	449	145	4	p	N	8
534	60	1.30	5119	10.72	10.60	22.14	9.50	9.75	8.7	286	420	-2	p	O	12
538	44	1.82	2801	10.35	10.26	22.05	9.02	9.03	12.4	163	177	3	ia	I	5
545	52	1.87	4635	10.78	10.79	22.17	9.46	9.60	17.0	376	364	1	p	I	7
575	40	0.81	5295	10.42	10.36	21.48	9.46	9.66	15.0	153	117	1	i	I	1, 2
602	44	1.32	2866	9.94	10.09	21.28	9.04	8.99	10.9	227	194	3.5		I	1, 2
617	30	1.33	4723	11.27	10.44	22.48	9.39	9.56	14.8	250	255	5	ia	I	7
620	44	3.46	1903	9.81	10.26	21.51	8.69	8.95	22.5	354	340	0.5		I	7
691	61	1.50	3297	10.14	10.36	21.62	9.14	9.00	8.4	143	100	4	p	I	1, 2
708	70	2.26	1897	9.74	9.85	21.11	8.65	9.03	27.1	242	197	5		I	5
731	49	2.39	1414	9.26		20.41		8.22	7.5		100	-1	i	I	1, 2
759	40	2.24	2066	9.76	10.16	21.82	8.78	8.70	10.7	208	167	5		I	1, 2
769	64	1.98	1663	9.80	9.98	21.09	8.62	8.31	6.8	207	89	1		I	5
799	62	1.90	3028	10.48	10.39	21.77	9.53	9.70	49.8	314	309	3	ia	I	7
848	60	0.82	12053	11.54		22.83		10.09	7.8		93	-2	ia	I	5
928	42	1.14	7316	11.07		22.65		10.33	5.9		259	-1	ia	N	8
938	74	1.75	5772	11.16		22.51	9.66	9.78	16.7	418	347	3	ia	I	7
1014			48893	12.14		24.01		10.70	0.2		130			N	13
1034	0	0.43	10047	11.33	10.39	22.65	9.94	10.46	26.4	261	450	6		I	7
1040	90	2.87	4914	10.31	10.73		9.59	9.47	1.8	440	500	4		N	14
1050	54	1.10	4853	10.55	10.37	21.60	9.40	9.63	16.7	217	250	1	i	I	1, 2
1066	65	1.79	3605	10.56	10.29	22.02		9.44	19.3		271	-1	p?	I	7
1073	21	1.04	6991	11.05	10.91	22.63	9.49	10.03	8.9	253	260	3	p	O	4
1088	21	1.75	4626	10.61	10.64	22.02	9.37	9.50	13.4	297	377	0	i	I	7
1093	48	1.10	4441	10.71		22.05	9.92	9.74	6.1	359	253	1	p?	S	5
1157	36	1.28	4495	10.09			9.31	9.02	8.0	259	110	0		NO	15
1194	53	1.88	4552	10.64	10.63	21.85	9.36	9.96	40.2	269	291	-2	i	I	7
1259	44	2.00	2159	10.30		21.53		8.46	9.5			-2		NO	11
1341	49	2.21	1132	9.09	9.57	20.14	8.23	7.95	6.4	186	155	6		I	1, 2
1365	40	0.76	5652	10.55	10.16	21.83	9.44	9.59	11.2	180	217	-2	i	I	1, 2
1376	90	2.90	1829	9.86	10.21	22.10	8.63	8.80	17.2	276	286	1		I	5
1379	58	1.46	2585	9.91	10.23	21.48	8.86	8.84	9.4	86	72	1.7		I	1, 2
1405	26	1.37	4963	10.56	10.91		9.48	9.83	11.1	281	280	-3	p?	O	4
1466	43	4.38	1226	9.45	9.96	20.80	8.37	8.47	17.8	201	120	5		I	7
1485	45	3.14	2308	9.73	10.40		8.91	8.79	10.5	286	240	3		I	1, 2

1. Contini (1996); 2. Contini et al. (1997); 3. Young et al. (1995); 4. Kandalyan et al. (1998); 5. Chini et al. (1992b); 6. Solomon et al. (1992); 7. Krugel et al. (1990); 8. Sanders et al. (1991); 9. Jackson et al. (1989); 10. Sofue et al. (1993); 11. Taniguchi et al. (1991); 12. Wiklind & Henkel (1989); 13. Sanders et al. (1988); 14. Heckman et al. (1989); 15. Taniguchi et al. (1990).

In the following discussion, the correlations were considered as real if the probability of random occurrence is less than 0.05. The flux densities have not been corrected for redshift because all objects, except Mkn 1014, have redshifts much less than 0.1.

2.2 The HI and H₂ gas kinematics

The gas kinematics of Mkn galaxies are studied by means of the statistical analysis of the HI and CO line widths. Figure 1 shows that there is a good correlation between WHI and WCO(correlation coefficient r=0.72 and its significance is p<0.0001). The relation presented in Fig. 1 indicates that the most part of the CO emission is likely to be co-planar with the large-scale galaxy disk. The same result was obtained previously by Heckman et al. (1989) for a sample of Seyfert galaxies. The dispersion in Fig. 1 may be due to several causes. Firstly, the HI observations are usually carried out with a much larger beam width of the radio telescope than that of CO observations. Hence, the number of individual clouds belonging to the beam area is much higher for the HI observations than for CO, so that the HI line width is a mean value from averaging over many clouds and the velocity dispersion among individual clouds may vary from one galaxy to another. Secondly, the dispersion in Fig. 1 could be also due to external and internal causes such as the environment of the galaxy and the starburst activity. It could be partly due to different behaviour of the gas rotation in galaxies. The least square fit of the HI and CO line widths data is

$$WCO = (0.71~\pm0.10)WHI + (59.4~\pm41.8).$$

We believe that, due to the gas motion, different samples of galaxies show different slopes in the HI and CO line width relation.

In Table 2 we report mean values of WHI, WCO, their standard deviation and number for different types of galaxies. Sofue et al. (1993) and Tutui & Sofue (1999) have suggested that tidal interaction could disturb the outermost but not the innermost regions of a galaxy. As a consequence, WHI for interacting galaxies will be much broader than that for isolated ones and no difference will be observed in WCO between the two types of galaxies. It can be seen from Table 2 that there are no significant differences between WHI, WCO for isolated and paired+interacting galaxies, although for paired+interacting objects, WHI is slightly higher than for isolated galaxies ( 458-377=81  $\mbox{km}~$s^-1). It is noticeable that unclassified galaxies have smaller values of both WHI and WCOthan those of isolated objects and significantly smaller than those for the paired+interacting galaxies. This fact is simply due to observational bias since, on the one hand, these objects are much fainter by global parameters such as $L_{\rm B}$, $L_{\rm fir}$, $M_{\rm HI}$, $M_{\rm H_2}$ (see Table 1) than classified galaxies, and, as a result, they have smaller line widths. On the other hand, because of the relative faintness of these objects, it is difficult to classify them. Nevertheless, when a part of unclassified galaxies were included in the group of isolated objects and another part in the group of paired+interacting galaxies, we still did not find significant differences for WHI and WCO between two main groups. Therefore interaction must have little influence on the HI line broadening and no influence on the CO line broadening in Mkn galaxies, although this problem needs a more detailed investigation based on a statistically significant and homogeneous sample.

 

 

Table 2: Mean values of WHI and WCO for Mkn galaxies.

Env	WHI	SD	N	WCO	SD	N
	$\mbox{km}~$s-1			$\mbox{km}~$s-1
Isolated	377	220	9	366	275	10
Paired+	458	237	15	370	190	22
interacting
Unclassified	278	117	20	245	124	20
All	359	200	44	321	195	52

Figure 1: The HI and CO line widths relation.

The observed integrated CO line profiles in external galaxies result from the convolution of the antenna beam pattern with intrinsic emissivity distribution for which the velocity varies across the beam. The line profile contains information on the distribution and kinematics of the gas.

In general, the HI and CO lines are broadened by the velocity dispersion among individual clouds and/or by galactic rotation. Most of galaxies have an HI line width larger than that of CO. The CO emission is generally concentrated within the central few kpc, while the HI gas distribution shows a depression in the central region of galaxy. The CO gas indicates the rotation and/or velocity dispersion among clouds in the innermost region including any rapidly rotating nuclear disk, whereas the HI gas indicates the rotation and velocity dispersion of the outer disk. Furthermore, superposition of individual clouds in the beam area is higher for HI observations than that for CO. Thus, in general, for a standard rotation curve (e.g. Sofue 1996, 1997, and the comprehensive review of Sofue & Rubin 2001), we should expect an HI line width larger compared to the CO line width. Observationally, there exist galaxies with FWHM of the CO line larger than that of the HI line (Kandalyan 1997; Tutui & Sufue 1999). In these galaxies there may exist a rapidly rotating nuclear disk and/or expanding molecular gas due to the input of kinetic energy from supernovae and stellar winds associated with a starburst (e.g. NGC 1365, 4258). When the molecular gas in the central part of a galaxy has clumpy structure (Sakamoto et al. 1999; Regan et al. 2001), then the velocity dispersion among individual clouds will increase the line width. In the case of lack of the high velocity HI clouds in the central region of a galaxy, the FWHM of the CO line will be larger than that for the HI line. A bar or oval distortion could lead to CO line broadening and increased the star formation activity in a galaxy. Tutui & Sofue (1999) argue that the CO line widths of the fast rotating galaxies tend to be larger than the HI line widths, while the HI line widths of slow rotating galaxies tend to be larger than the CO line widths.

Let us now discuss the difference between the HI and CO line widths. Figure 2 shows the histogram of (WHI-WCO) for Markarian galaxies. One can see that most of galaxies have WHI >WCO. However, according to Fig. 2, there exist galaxies with WHI<WCO. For the galaxies Mkn 201, 353, 534, 1034, this difference is significant (higher than 0.01) and it is about 0.05 for Mkn 1088 and 1365. The inequality WCO>WHI may indicate the existence of a rapidly rotating nuclear disk in the galaxy and, as a consequence, the rotation curves of these galaxies could have a peak in the central region (<1 kpc), as in case of NGC 3031, 3079, 5236, 6946 (Sofue 1996, 1997). The high angular resolution observations of the HI and CO are essential in testing this hypothesis.

The number of Mkn galaxies with a broad CO line width is insufficient for statistical analysis, but it is interesting that these galaxies are either barred or peculiar objects regardless of whether the galaxy is isolated, interacting or merging. Note that the velocity in barred spirals increases more steeply with radius than in unbarred ones. In the circumnuclear region of barred galaxies, the velocity field of the CO gas can have many different behaviours. For example, the velocity field in NGC 3504 is consistent with purely circular motion (Kenney et al. 1993), while in NGC 4314, both circular and non-circular motions have been observed (Benedict et al. 1996). The disk rotation curves of barred galaxies show dispersion larger than those of normal galaxies (Sofue et al. 1999). Recently Regan et al. (1999) have detected the high velocity (higher than circular velocity) streaming CO gas in seven barred galaxies. Objects with relatively broad CO emission will be very important for the study of the gas kinematics and dynamics of the central region.

Figure 2: Distribution of the HI and CO line widths difference.