3 Analysis

3.1 Radio continuum

Figure 2 shows the cleaned radio continuum map of NGC 3310 at full resolution. The extended source of emission includes nucleus, central ring and spiral arms; its peak surface brightness is 63 mJy beam^-1. The 5.5 mJy beam^-1 point source, visible $\sim$1$^\prime$ south-east of the nucleus, is probably a background source. The position of the nucleus cannot be determined accurately for such an extended source. The value of the continuum flux at 1.42 GHz (Table 3) agrees with those published by Lequeux (1971) and by Duric et al. (1986). The total power is $21.85\pm0.03$ ( $\log~(P_{1.42 {\rm GHz}}$/ W Hz^-1)).

Figure 2: Full resolution ( $14\hbox{$.\!\!^{\prime\prime}$ }2\times17\hbox{$.\!\!^{\prime\prime}$ }7$) map of the radio continuum emission from NGC 3310 at 1.42 GHz. The rms noise is $0.29\ \mbox{mJy}\ \mbox{beam}^{-1}$, contour levels are (first:last:increment) 1:6:1, 8:17:3, 23:51:7 and 59  $\mbox{mJy}\ \mbox{beam}^{-1}$. The H$\alpha$ image (van der Kruit & de Bruyn 1976) is shown in greyscale.

Figure 3: Global 21 cm line profile of NGC 3310 (solid line). The dots show the northern tail, the crosses the southern tail and the circles the H I disk.

 

 

Table 3: Integral H I properties and the radio continuum flux of NGC 3310.

Quantity		Units	Value
$\int S\ {\rm d}v$		Jy km s-1	$69\pm4$
$M_{\rm H{\sc i}}$		$10^{9}\ {M}_{\rm\odot}$	$2.8\pm0.2$
$S_{1.42\ \mbox{GHz}}$		Jy	$0.34\pm0.01$

Figure 4: H I channel maps of NGC 3310. The beam size (HPBW) is $29\hbox{$.\!\!^{\prime\prime}$ }9\times30\hbox{$.\!\!^{\prime\prime}$ }7$. The contour levels are -3.2, -1.6, 1.6 ($\sim$ $2\times {\rm rms}$ noise), 3.2, 4.8, 6.3, 7.8, 15.7, 23.6 and 31.4 mJy beam-1. The shading shows the faint extended emission in the outer parts on a logarithmic scale up to 6.5 mJy beam-1 at a resolution of $60\hbox{$.\!\!^{\prime\prime}$ }9\times63\hbox{$.\!\!^{\prime\prime}$ }0$. Also the optical image (top left) and the radio continuum image used for subtraction (bottom right) are shown. The radial velocities (in kms-1) are heliocentric.

3.2 Anomalous HI

The H I line flux was determined in each channel map at 60 $^{\prime \prime }$ resolution. The resulting global H I profile is shown in Fig. 3. It is similar to that obtained by Mulder et al. (1995). The asymmetric structure and the remarkable tail on the low velocity side clearly point at some anomaly in the H I distribution and/or kinematics. The integral quantities derived from the global profile are listed in Table 3.

The channel maps (Fig. 4) show that the bulk of H I coincides with the bright optical disk and has the characteristic pattern of differential rotation. There are, in addition, two extended features, one on the north-west side visible in the velocity range 870 to 953 kms^-1 and the other to the south, clearly visible (shaded) at velocities 1003 to 1069 kms^-1. Both have already been noticed and reported by Mulder et al. (1995). The better sensitivity of the data presented here makes it possible, however, to significantly improve the study of their structure and kinematics. In the following, these two extended features will be referred to as the northern and the southern tail.

a) Northern tail

Figure 5: Map showing the H I tails of NGC 3310 overlayed on the optical picture. The beam size is $60\hbox{$.\!\!^{\prime\prime}$ }9\times63\hbox{$.\!\!^{\prime\prime}$ }0$. The contour levels are 0.4, 0.8, 1.2, 1.6, 2.0, 2.4, 3.0 and $3.6 \times 10^{20}$ cm-2. The velocity ranges for the northern and the southern tail are indicated.

The H I extension to the north-west (Fig. 4) coincides with the already mentioned and well-known "arrow''. One cannot fail to notice the continuity in space and velocity of this feature with the emission in the channel maps at lower velocities, from 854 to 804 kms^-1. It should also be noted that these are precisely the velocities of the anomalous tail in the global H I profile. It is therefore natural to associate the H I in the anomalous 804-854 km s^-1 velocity range with the anomalous H I pointing away from the main body (the "arrow'') in the adjacent, higher velocity channels 870 to 953 kms^-1. The resulting structure has the shape of a tail (see Fig. 5) located on the northern edge of the disk, slightly curved and elongated from the east to the north-west. It has been obtained by adding the H I over the whole velocity range 804 to 953 kms^-1 and by taking, at velocities 887 to 953 kms^-1, only the emission from the "arrow''. There is a striking coincidence of this H I tail not only with the optically bright knots of the "arrow'' itself but also with the bright compact knots seen along a curve on the northern side of the bright disk of NGC 3310. Since the tail is unresolved at 60 $^{\prime \prime }$, the same procedure as described above was repeated at 30 $^{\prime \prime }$ and the result is shown in Fig. 6a. The coincidence with the optical knots is even clearer, suggesting a physical association of the knots with the H I tail. These knots should then have the same velocity as the H I; but according to the H$\alpha$ data published by Mulder & van Driel (1996), their velocities seem to be around 950 km s^-1, difficult to reconcile with the velocity of the H I indicated here.

The kinematics and structure of the tail are illustrated in the position-velocity map of Fig. 6b which was constructed along the path marked by the crosses in Fig. 6a. The distance along the tail in Fig. 6b is measured with respect to the most eastern marker. The figure shows the H I of the disk, which is centered at 950 kms^-1, and the tail (shaded), which is in the velocity range 800 to 940 kms^-1. There is a dip in the tail at a distance of 150 $^{\prime \prime }$ and a velocity of 850 kms^-1. The main properties of the tail are listed in Table 4. Its H I mass is about 8% of the total hydrogen mass of NGC 3310.

Clearly, if the above analysis is valid and it is correct to connect the kinematically anomalous H I with that of the "arrow'' as we have done, a completely new physical picture emerges: instead of a straight jet pointing outward from the nucleus as suggested before (Bertola & Sharp 1984), we have a curved tail-like structure attached to the northern edge of the bright optical disk.

b) Southern tail

The channel maps in Fig. 4 show an extended, peculiar feature (shaded area) on the southern side of NGC 3310 at radial velocities ranging from 953 up to $1069~\mbox{km}\,\mbox{s}^{-1}$. It has a somewhat patchy, but coherent tail-like structure (see also Fig. 5) connecting smoothly to the H I disk on its western side. The southern structure shown in Fig. 5 was obtained by adding all channel maps in the above velocity range.

Figure 6: a) 30 $^{\prime \prime }$ contourmap of the northern tail overlayed on the optical picture. The contour levels are 1, 2, 3, 4, 5, 6 and $7\times 10^{20}$ cm-2, b) position-velocity map along the track from east to west marked in a) following the ridge of the northern tail. The contour levels are as for the channel maps (Fig. 4). In this position-velocity diagram the tail is shown shaded.

Figure 7: a) The southern H I tail is represented in contours (same as in Fig. 5). The shading shows the total H I density distribution of NGC 3310 at 60 $^{\prime \prime }$ resolution (obtained by integrating over all velocities), b) position-velocity map along the track following the ridge of the tail from north to south, as marked in a). The contour levels are -2.1, 2.1, 4.3, 6.4, and 10.7 mJy beam-1.

Figure 7a shows the tail and the total H I at 60 $^{\prime \prime }$ resolution. The crosses mark the path along which the position-velocity map shown in Fig. 7b was constructed. The distance along the tail in Fig. 7b is with respect to the most northern marker. The figure shows a clear continuity in both space and velocity from the inner to the outer regions. The tail seems to be an extension of the western part of the H I disk (the emission closer to the bright disk has been omitted because of confusion). Its main properties are given in Table 4. Its H I mass is at least 9% of the total hydrogen mass of NGC 3310.

 

 

Table 4: H I properties of the tails of NGC 3310.

Quantity	Units	Northern	Southern
$M_{\rm H{\sc i}}$	108 $M_{\rm\odot}$	$2.3\pm 0.2$	$2.7\pm 0.2$
Length	kpc	23	51
$\left(N_{\rm H{\sc i}}\right)_{\rm\mbox{max}}$	1020 cm-2	7.5	$\sim$1.5
$\sigma_{\rm H{\sc i}}$	km s-1	17	13

In addition to the two well-developed H I tails, Fig. 5 also shows hints of an isolated feature to the south-east of NGC 3310, visible (faint shaded areas) in Fig. 4 at velocities of 1053 and 1069 kms^-1. This could be part of the southern tail described above. The present observations, however, are not sensitive enough to be sure of the reality of this feature.

3.3 HI disk

The overall H I density distribution and the velocity field in and around NGC 3310 are shown in Figs. 9a and b. More detailed maps of the H I disk, at 20 arcsec resolution, are presented in Figs. 9c and d. The high-resolution total H I map was obtained by defining the area of the emission for each channel map using the lower-resolution maps as masks. The velocity field was obtained by taking the density weighted mean with a 1.7 mJy beam^-1(2$\sigma$) cutoff. In the construction of these maps, the emission from the northern and southern tails, clearly visible in the 60 $^{\prime \prime }$ channel maps, was masked out in order to have a clearer picture of the disk structure and kinematics.

In the 60 $^{\prime \prime }$ map, the central surface density reaches $\sim$ $2.4\times 10^{21}$ cm^-2 which corresponds to $\sim$ $11~M_{\rm\odot}$ pc^-2 in the plane of the galaxy. This is similar to the values found for normal high surface brightness galaxies (Broeils & van Woerden 1994; Rhee & van Albada 1996. The 20 $^{\prime \prime }$ resolution map shows that the peak surface density is actually $\sim$ $4.5\times 10^{21}$ cm^-2 and is reached about 30 $^{\prime \prime }$ south of the optical center.

The 20 $^{\prime \prime }$ map (Fig. 9c) shows a disk with a bright inner part and a large depression centered $\sim$8 $^{\prime \prime }$ ($\sim$500 pc) south-east of the optical center. This depression coincides with the brightest region of Far UV emission (Smith et al. 1996). The bright inner part is surrounded on all sides by low surface density structures (average densities about $5~M_{\rm\odot}$ pc^-2). In Fig. 8 this H I map is compared with the optical image. The highest H I density features appear to coincide with the extensions of the optical spiral arms (compare Figs. 8 and 9c). The outer low surface brightness H I seems to coincide only partly with the optical ripple (the "bow'') in the north-west and on the southern side.

Figure 8: 20 $^{\prime \prime }$ H I map (HPBW = $20\hbox{$.\!\!^{\prime\prime}$ }0\times20\hbox{$.\!\!^{\prime\prime}$ }0$) overlayed on the optical picture (Fig. 1). The contour levels (first:last:increment, in units of 1020 cm-2) are 1.5, 3:12:3, 18:42:6 and 45 as in Fig. 9c.

Figure 9: a) Total H I map ( $HPBW = 60\hbox{$.\!\!^{\prime\prime}$ }9\times63\hbox{$.\!\!^{\prime\prime}$ }0$). The contour levels (first:last:increment, in units of 1020 cm-2) are 0.2:1.4:0.3, 2.0:4.4:0.6, 5.6:9.2:1.2 and 11.6:23.6:2.4, b) velocity field ( $HPBW = 60\hbox{$.\!\!^{\prime\prime}$ }9\times63\hbox{$.\!\!^{\prime\prime}$ }0$). The contour levels are in steps of 20 kms-1 and the thick contour represents $v_{\rm sys}$ at 1006 kms-1 (the northern side is approaching) c) H I map ( $HPBW = 20\hbox{$.\!\!^{\prime\prime}$ }0\times20\hbox{$.\!\!^{\prime\prime}$ }0$), disk only. The contour levels are (in units of 1020 cm-2) 1.5, 3:12:3, 18:42:6 and 45 d) velocity field ( $HPBW = 20\hbox{$.\!\!^{\prime\prime}$ }0\times20\hbox{$.\!\!^{\prime\prime}$ }0$). The contour levels are in steps of 20 kms-1 and the thick contour represents $v_{\rm sys}$ at 1006 kms-1. The crosses in the panels mark the position of the optical center. The velocity fields are only defined where the surface densities are larger than the values of the second contour in the total H I maps.

The motion of the H I disk is clearly dominated by differential rotation although there are irregularities, especially in the outer parts (Figs. 9b and d). At 60 $^{\prime \prime }$ resolution such irregularities are partly due to the presence of the anomalous H I.

The H I velocity dispersion is unusually large (ranging from 20 to 40 km s^-1), especially in the inner high-density regions which coincide with the stellar disk. H I position-velocity maps taken from the 20 $^{\prime \prime }$ data at various position angles (see e.g. Fig. 10b) show this very clearly and reveal the presence of faint velocity tails even extending to the quadrant of forbidden velocities (across the systemic velocity line). In the same areas of the disk, H II regions also show large (30-40 kms^-1) velocity dispersions and large deviations from circular motion (van der Kruit 1976; Grothues & Schmidt-Kaler 1991; Mulder & van Driel 1996).

A tilted-ring model (cf. Begeman 1989) was fitted to the velocity field to determine the center of rotation and the inclination angle. This led to an inclination of $56\pm 7$ degrees for the H I disk, significantly larger than found for the optical disk (Table 1).

The azimuthally-averaged radial density distribution of the H I was calculated from the data at 30 $^{\prime \prime }$ resolution by averaging the signal in circular rings in the plane of the galaxy. The inclination angle was kept fixed at 56 degrees and the major axis position angle at 150 degrees. The H I distribution is approximately exponential. The scalelength ( $h_{H{\sc i}}$) and the radius at a level of $1~M_{\rm\odot}$ pc^-2 ( $R_{H{\sc i}}$) are given in Table 5. They are similar to those found for galaxies of the same Hubble type (Sbc) as NGC 3310 (Verheijen 1997).

 

 

Table 5: H I and optical parameters for NGC 3310.

Quantity	Units	Value
inclination angle (H I)	degrees	$56\pm 7$
position angle (H I) (N $\rightarrow$E)	degrees	$150\pm5$
$v_{\rm sys}$ (heliocentric)	km s-1	$1006\pm4$
$M_{\rm H{\sc i}}^{\rm disk}$	109 $M_{\rm\odot}$	$2.2\pm0.1$
$h_{\rm H{\sc i}}$	arcsec	$48\pm4$
$R_{\rm H{\sc i}}$	arcsec	$109\pm5$
$R_{\rm T}^{0}$ mag	mag	$10.42\pm0.07$
LR1	$10^{10}\ {L}_{R,\odot}$	$0.64\pm0.04$
$r_{\rm e}$	arcsec	$12\pm2$
$\mu_{\rm e}$	R-mag arsec-2	$18.22\pm0.05$
$M_{\rm lum}$ (maximum disk)	1010 $M_{\rm\odot}$	0.2
$M_{\rm tot}$ (inside $r=110\hbox{$^{\prime\prime}$ }$)	1010 $M_{\rm\odot}$	2.2
$M_{\rm H{\sc i}}^{\rm disk}$/LR	$M_{\rm\odot}$/ $L_{R, \odot}$	$0.34\pm0.02$
$M_{\rm tot}$/LR	$M_{\rm\odot}$/ $L_{R, \odot}$	3.4
$M_{\rm H{\sc i}}^{\rm disk}$/ $M_{\rm lum}$		1.1
$M_{\rm H{\sc i}}^{\rm disk}$/ $M_{\rm tot}$		0.1

1.

The R-band magnitude is converted to luminosity in solar units using $M_{R,\odot} = 4.31$.

The tilted-ring model fits were also used to derive the rotational velocity. Inclination and position angles were kept fixed. The rotational velocities obtained for an inclination angle of 56 degrees, a position angle of 150 degrees and systemic velocity of 1006 kms^-1 and estimated for each side separately, are presented in Fig. 10a as dots (approaching side) and crosses (receding side). The H I rotational velocity is $\sim$60 kms^-1at 15 $^{\prime \prime }$ from the center, just outside the optical ring, and slowly increases further out. Beyond the optical disk, the velocity of the approaching side rises up to 120 kms^-1 whereas the velocities of the receding side level off at 80 km s^-1. The curve derived from the H$\alpha$ observations (van der Kruit 1976) is also shown (rescaled using the H I inclination). It shows solid body rotation in the inner region up to the starburst ring at $\sim$10 $^{\prime \prime }$ reaching a maximum of $\sim$105 km s^-1. This is followed by a sharp drop-off down to 60 kms^-1 and a slight increase up to 80 kms^-1 at 70 $^{\prime \prime }$. The sharp drop in the curve is steeper than Keplerian, indicating that there are non-circular motions present in the inner region (van der Kruit 1976).

Figure 10b shows the rotation curves of the approaching and receding sides superposed (after projection to $v_{{\rm rot}}\sin i$) on the H I position-velocity map along the major axis. The projected H$\alpha$ velocities (van der Kruit 1976) are also shown (dotted line). There is good agreement between the H I and H$\alpha$: although the H I data are too coarse to get a good estimate of the rotation near the center, the lowest contours in the H I position-velocity map show that the H I motion is consistent with the H$\alpha$ velocities. Figure 10b shows clearly that, in spite of its overall rotation, the H I has a peculiar kinematics characterized by a large velocity dispersion and asymmetric profiles. The H I rotation curve derived here has large uncertainties, especially because of the large deviations from circular motion. This uncertainty is of order 20-30 kms^-1. However, the agreement of the H I and H$\alpha$ curves between 20 and 60 arcsec (Fig. 10) indicates that the amplitude of the projected rotation curve adopted here is probably correct. The optical and H I inclination and position angles (Tables 1 and 5) are also very uncertain and do show large discrepancies.

Because of all these problems and uncertainties the standard analysis with the well-known decomposition in luminous (stars and gas) and dark components (Begeman 1989) may be doubtful. In the following, the results obtained on the mass distribution, the total mass and the mass-to-light ratio should therefore be taken with caution.

The R-band surface brightness profile (Fig. 11, dots) was derived from an optical (R-band) image of NGC 3310 (Swaters et al. 2001) using the inclination and position angles as determined from the H I (Table 5). It is best described by an R^1/4 law (Fig. 11, the effective parameters $\mu_{\rm e}$ and $r_{\rm e}$ are given in Table 5), except for the inner 10 $^{\prime \prime }$ (the compact nucleus and the starburst ring). For comparison an exponential disk fit to the bright disk gives a scalelength $h_{R} = 9\pm1\hbox{$^{\prime\prime}$ }$ ($\sim$0.6 kpc) and $\mu_{0}=16.82\pm0.05$ R-mag arcsec^-2. The surface brightness profile as derived using the inclination and position angle of the optical disk is also shown (circles).

Figure 10: a) The solid dots and crosses give the H I rotation velocities of the approaching and receding sides respectively, the solid curve shows the mean H I rotation curve. The dashed curve shows the maximum disk (stars & gas) rotation curve, the dotted one is that of the H$\alpha$ obtained by van der Kruit (1976), b) Position-velocity map along the major axis (position angle 150 degrees) at 20 $^{\prime \prime }$ resolution. Contour levels are -1.7, 1.7, 3.4, 5.1, 8.5 and 16.9 mJy beam-1. The dots and crosses give the projected H I rotational velocities for the approaching and receding sides. The dotted curve is from van der Kruit (1976).

Figure 11: R-band surface brightness profile of NGC 3310. The dots are for the inclination and position angle of the H I (Table 5), the circles for the inclination and position angle of the H$\alpha$ (Table 1).

The rotation curve for the disk was calculated from the R-band photometric profile (Fig. 11, dots) assuming a truncated disk potential (Casertano 1983) and a mass-to-light ratio constant with radius. The rotation curve of the gas was derived from the H I density distribution after multiplication by a factor of 1.32 to correct for the presence of helium. The maximal rotation curve of the luminous matter (gas & stars) is shown in Fig. 10a (dashed curve). A clear discrepancy with the observed rotation curve is visible in the outer parts. Such discrepancies are usually taken to be evidence for the presence of a dark halo. In the inner ring there is a large difference between the maximal rotation curve and the H$\alpha$ curve. This would imply a mass discrepancy also in the inner region and the presence of a dark mass of about $5\times 10^{9}~M_{\odot}$. However, the sharp drop in the H$\alpha$ curve is steeper than Keplerian (van der Kruit 1976), indicating that at least part of the discrepancy is caused by non-circular motions.

The mass derived for the maximum disk and the total mass out to 110 $^{\prime \prime }$ (=7.1 kpc) are given in Table 5. When compared to regular spiral galaxies of similar rotational velocity (e.g. Verheijen 1997) NGC 3310 has a rather large R-band luminosity (Table 5) and low values for the mass-to-light ratio of the maximum disk ( $M_{\rm lum}/L_{R} = 0.3~M_{\odot}/L_{R, \odot}$) and for the global mass-to-light ratio inside 110 $^{\prime \prime }$ ( $M_{\rm tot}$/L_R = 3.4 $M_{\odot}$/ $L_{R, \odot}$). The amplitude of the rotation curve may have been underestimated due to our choice of inclination angle. This may have led to a factor 2 underestimate of the maximum disk and total masses.