4 Discussion

   
4.1 Detections of radio halos from our data

Four galaxies were excluded from the total sample of 15 objects for various reasons:

• In the case of NGC2820 it was found that it has nearby interaction partners. Therefore, it is not clear whether energy input by active SF into its disk or a gravitational drag might dominate the energy balance of any observed disk-halo interactions;

• The inclination angle of NGC4527 turned out to be too low to allow for the kind of studies intended here;

• Both NGC5073 and NGC7541 show signs of previously unlisted AGNs (see below), which we wanted to exclude from the beginning.

 

 

Table 6: Detections of halo emission.

Galaxy	Radio	H$\alpha$
NGC1055	no	--
NGC1406	yes	--
NGC1421	no	no
NGC1511	yes	yes
NGC2748	no	--
NGC3175	yes	no
NGC3437	no	--
NGC3717	no	--
NGC4700	yes	yesa
NGC7090	yes	yesa
NGC7462	yes	yesa

Note to Table 6: ^a Rossa (2001).

A "clean'' sample of 11 galaxies remains. Of these the following 6 have positively detected radio halo emission: NGC1406, NGC1511, NGC3175, NGC4700, NGC7090 and NGC7462, see Table 6. For NGC1055, NGC1421, NGC2748, NGC3437, NGC3717, there is no or only marginal evidence. Thus, amongst the galaxies fulfilling the criteria for studies of dependences of their halo properties on their level of SF in the disks (i.e., those with  , no AGNs and no nearby interaction partners) the current detection rate is 6 out of 11, i.e. 55%.

The absence of clear evidence for the presence of halos in the remaining galaxies can, as indicated above, have different reasons:

• There is no halo because of too little energy input from the underlying disk;

• The inclination of the galaxy is too low. This cannot only lead to an apparently thick disk, but can also hamper the separation of residual high-z emission from that widened disk;

• The angular resolution of our data is insufficient. The need for good angular resolution is demonstrated by a comparison of the two observations of NGC3175 in Figs. 25 and 34 (more details are given in Sect. 4.2.1). From a marginal case in the former, twice the angular resolution leads to a clear detection with well-constrained halo scale height measurements. In particular, the observations of NGC3437 might be affected by this problem. Insufficient angular resolution and at the same time an inclination of $i < 90^\circ$ can exacerbate the problem;

• The thin disk is not visible, because weak. Two of the galaxies in the present clean sample have f₆₀/f₁₀₀ ratios >0.4, but require only a single-exponential model. In principle, if one interprets this in terms of the absence of halo emission, this is a contradiction to our hypothesis. However, just these two galaxies require fits to their "disks'' that are unusually wide compared to the thin disks in galaxies with spatially separable disk plus halo components (Table 4). This might suggest either a relatively low inclination angle, which can mimic the presence of a "thick'' disk (but is unlikely because of the galaxies' optical appearance), or the presence of two unresolved components, of which the wide one dominates the overall emission distribution perpendicular to the disk. This is a reasonable explanation of our results, because the scale height of the z distribution of NGC3437 and NGC3717, of 1.2 to 1.9 kpc, respectively, is more similar to those of the detected halos than the scale heights of the detected thin disk components. Therefore, these galaxies might have radio halos that just require higher angular resolution to render possible the spatial separation of halo and thin disk emission.

Consequently, an FIR colour of $f_{60}/f_{100}\ > 0.4$ is indeed a good search criterion for galaxies with a gaseous halo.

   
4.2 Evidence for halo emission from different wavebands

In addition to the synchrotron radio continuum from relativistic CR electrons there are other tracers of gaseous halos around spiral galaxies, of which the most important are H$\alpha$ recombination radiation of warm ionised gas and soft X-ray emission from a hot thermal plasma (cf. Dahlem 1997).

   
4.2.1 Previous radio observations

In the following we briefly summarise those previously published radio continuum images that are relevant for searches of extraplanar emission in the galaxies presented here.

NGC1421:   Irwin et al. (1999) found some evidence for extraplanar emission in NGC1421 from their VLA C array 1.4 GHz radio continuum image (see their Fig. 4). The authors provided us with their data, which were combined with our D array visibilities to obtain a map that contains the full flux and has improved angular resolution (as displayed in Fig. 3).

NGC2748:   A 15'' resolution 1.465 GHz map of NGC2748 by Hummel et al. (1985) might indicate the presence of radio continuum emission away from its disk plane (their Fig. 1c). However, these authors quote a lower total flux than measured by us. Due to missing short spacings (and thus missing extended flux) these data cannot be used for the present study.

NGC2820:   The VLA C array image by Hummel & van der Hulst (1989) has a higher angular resolution than ours (15'' [their Fig. 1] compared to $62''\times 41''$; Fig. 6, above), but lower sensitivity. Based on a z profile as used by us here (their Fig. 2), Hummel & van der Hulst (1989) found that NGC2820 has a thick radio disk or halo at 1.465 GHz. Since these authors did not report an exponential scale height for the halo emission, we rely here on our own measurement (note that this galaxy has been removed from the sample anyway). The fact that Hummel & van der Hulst find evidence for the presence of a halo, while there is none in our data, demonstrates the need for sufficient angular resolution.

NGC3175:   A 1.49 GHz radio continuum map of NGC3175 by Condon et al. (1996) displays three maxima in the galaxy disk, one at the centre and one each about 45'' on either side of it, thus coinciding with the most prominent H II regions in the H$\alpha$ image by Ryder & Dopita (1994). The contour map displayed in Condon et al. (1996) might also indicate halo emission above its central region. This VLA C array map has a higher angular resolution (15'' compared to $43''\times 33''$) than ours, but lower sensitivity. It exhibits a low axial ratio of the radio continuum emission, suggesting that there might be a relatively small outflow from the nuclear region. Since it recovers the total flux (the same within the error margins as our measurement; see Table 3), Condon et al.'s image can be used for a study of the z structure of the emission distribution.

Because of the very different integration times, it is not possible to combine Condon et al.'s data with ours. However, the image being available via NED, we have retrieved it and used it to produce a second z profile. This higher-resolution z profile is displayed separately in Fig. 34. The plot reassuringly reproduces the major features from Fig. 25, however in more detail. The distribution of excess emission beyond the thin disk is slightly asymmetric, being brighter on the south-east side (negative offset values), as already visible in our DnC array data. But now it is much clearer that this excess emission, in particular also that on the north-west side, is indeed significant. The results from the fitting process are collected in Table 4.

NGC3437:   Condon et al. (1990) presented a high-resolution 1.49 GHz image of NGC3437. However, since it does not recover the total flux of the galaxy, it is not suitable for investigations of the extended emission distribution, including the z structure perpendicular to the disk plane.

NGC5073:   We note here that a 1.49 GHz radio image of NGC5073 by Condon et al. (1990) exhibits a compact central source that is unresolved at a resolution of about 5''. This is relevant in the context of the H$\alpha$ data of this galaxy mentioned below. Since it does not recover the full extended flux of the galaxy, the radio map cannot be used for a study of the large-scale emission distribution along the minor axis.

NGC7090:   Two "spurs'' of radio emission above the disk of NGC7090 were detected by Harnett & Reynolds (1985) at 843 MHz (see their Plate 3). Our maps are more sensitive and have better angular resolution thus showing more extended halo emission. The brightest spur north-east of the central region, now embedded in extended emission, is visible in our 1.43 GHz map (cf. Fig. 13) as kinks in the isophotal contours, which can be traced from close to the disk plane out to the detection limit of the halo.

NGC7462:   There is a tentative detection of extraplanar radio continuum emission from NGC7462 in a 1.49 GHz VLA map by Condon et al. (1987). However, the angular resolution (of 1') and sensitivity of these snapshot observations were insufficient to make a firm statement. Our detection is much more conclusive, in particular because the result comes from observations at two independent frequencies.

NGC7541:   Condon et al. (1990) published a snapshot 1.49 GHz map of NGC7541, with a resolution of 15''. It exhibits a dominant unresolved central source, which might hint at the presence of an active nucleus. Since this radio image does not recover all extended source flux, it is not used as part of the present investigation.

   
4.2.2 H$\alpha$ line imaging

5 of the 15 galaxies studied here are also in the sample by Lehnert & Heckman (1995): NGC1511, NGC2820, NGC4527, NGC5073 and NGC7541. Three of these, namely NGC1511, NGC4527 and NGC5073, were imaged in H$\alpha$ line emission. In addition, H$\alpha$images of a few more individual galaxies can be found in the literature.

NGC1421:   An unpublished H$\alpha$ image by Dettmar (priv. comm.) exhibits numerous H II regions in the disk of NGC1421, indicating a two-arm spiral structure and an inclination of $i < 90^\circ$. No extraplanar H$\alpha$ line emission was detected. However, this might be due to a lack of sensitivity.

NGC1511:   The H$\alpha$ image of NGC1511 by Lehnert & Heckman (1995) shows a disturbed structure, with H II regions that are located outside the thin disk plane. There are also indications of diffuse H$\alpha$, which apparently does not arise from the central disk plane, but there is no direct evidence for halo emission. The disturbance of its disk might arise from interactions with one of its partners, NGC1511A or B, or just be its intrinsic structure. With an absolute R magnitude of -18.6 (Lehnert & Heckman 1995) NGC1511 is a low optical luminosity, low-mass galaxy, in which disturbances are known to be quite normal (compare, e.g., with NGC1569, NGC4449 or NGC2188).

NGC3175:   An H$\alpha$ image by Ryder & Dopita (1994) shows bright H II regions at the position of the nucleus and what appears to be a starburst ring with a radius of 3.5 kpc around it. The H II regions at the tangential points of this ring are apparently the brightest. These might also be "thick'', i.e. extended in the direction perpendicular to the disk plane. However, no extended diffuse H$\alpha$ emission is visible, especially away from the disk plane. Note that NGC3175 does not exhibit any signs of ongoing star formation outside the starburst ring. Its outer disk has a very red colour (Ryder & Dopita 1994) and is H I deficient (Dahlem et al. 2001).

NGC4527:   The H$\alpha$ image of NGC4527 by Lehnert & Heckman (1995) shows no obvious signs of extraplanar emission. Instead, it indicates that the disk is not inclined exactly edge-on. From its optical axial ratio of 3 Tully (1988) derived an inclination angle of about $i\ = 68^\circ$, which has been taken into account in our representation of the radio emission from the disk in Fig. 28 and which is the reason for removing the object from the present sample.

NGC4700:   NGC4700 was observed by us (Rossa 2001) and the resulting image will be presented separately. Clear evidence for extraplanar H$\alpha$ emission is visible in our frame; therefore the corresponding entry was made in Table 6.

NGC5073:   In the H$\alpha$ image of NGC5073 by Lehnert & Heckman (1995) one can see little diffuse emission above the nuclear area and a strong point source in the centre. Together with the unresolved nuclear radio continuum source, this might hint at the presence of a previously unclassified active nucleus, which could explain why a high f₆₀/f₁₀₀ flux ratio is observed and the radio emission is unresolved by our data, while there is no indication of a halo.

NGC7090 and NGC7462:   Both galaxies were observed and extraplanar H$\alpha$ emission clearly detected (Rossa 2001). These results will be presented at a later time, together with those on NGC4700.

Resume:   The small number of H$\alpha$ detections is probably in most cases due to sensitivity problems, because the images available in the literature were not taken for dedicated searches of low surface brightness extraplanar emission. Long integration times are required for attempts to detect such emission.

   
4.2.3 Soft X-ray imagery

Data existing in archives.   ROSAT archival data exist for NGC1406, NGC2820, NGC4527; however, they do not contribute anything new to the current investigation. NGC1406 is detected, but unresolved; a by-eye inspection of the data reveals no detected emission from either NGC2820 or NGC4527.

Einstein observations of NGC1421 show weak emission from its disk, but also from a "tail'' to the south of the optically visible disk and also west of the nuclear area, thus perpendicular to the disk plane, where the extreme colour stretch used by Fabbiano et al. (1992) for the underlying optical image might suggest the presence of a stellar tidal arm.

Future observations.   Of the present sample, Chandra observations of NGC1055 have been approved. We will obtain XMM-Newton Guaranteed Time observations of NGC1511 and NGC5073, which will be presented elsewhere in due course.

4.2.4 Summary of observational evidence

Considering all observations listed above of tracers of gaseous halos, 6 out of the 11 galaxies presented here show signs of extraplanar emission in at least one waveband. Different components of the halo ISM in the target galaxies were detected in four cases, as previously done in more nearby systems (see e.g. Dahlem 1997). A list of the detection/non-detection of extraplanar radio and H$\alpha$ emission is provided in Table 6.

Thus, it appears that the existence of gaseous halos around late-type spiral galaxies is indeed not as uncommon as it appeared in the past. Rather, the search criteria are now optimised. Also the high detection rate by Irwin et al. (1999) of >90% fits into this scenario.

FIR brightness and in particular "warm'' FIR colours, i.e. high f₆₀/f₁₀₀ flux ratios, have turned out to be a very effective search criterion (Heckman et al. 1990; Lehnert & Heckman 1995). This is also born out by the fact that all FIR-warm nearby edge-on starburst galaxies studied by us previously in the soft X-ray regime (D98) exhibit diffuse extraplanar X-ray emission. A somewhat lower detection rate in the present sample can be expected, because we include here objects at larger distances and thus with lower flux densities and surface brightnesses than before. With values of in some cases 5-9 kpc (Table 4) also the spatial resolution of our data is not always sufficient yet.

   
4.3 On the origin of gaseous halos

   
4.3.1 Making sure that star formation dominates the energy input into the ISM

As outlined by Dahlem (1997), several processes can contribute to the creation of gaseous halos around late-type spirals. In order to make sure that only star-formation related energy input is taken into account, galaxies with AGNs and closely interacting systems have been removed from the original sample above. Many starburst galaxies are interacting, or reversely, there is an overabundance of starbursts in interacting galaxies (cf. Hummel et al. 1990; Lutz 1992). In the case of distant encounters one can hope that the interaction has only caused minor disturbances of the gas in the galaxies, leading to the accretion of gas near their inner Lindblad resonance (Combes 1987) or turnover point of galactic rotation (Lesch et al. 1990) and subsequently to the onset of the observed starbursts, while the starbursts themselves dominate the energy balance at the time of the observation. This leaves galaxies that have high f₆₀/f₁₀₀ flux ratios because of SF-related heating of their dust, with approximately unperturbed gravitational potentials. SF-related heating sources are photo-ionisation, shocks and/or turbulent mixing layers, but in principle all energy comes from processes relating to the evolution of high-mass stars (winds and type II supernovae; Leitherer & Heckman 1995; Leitherer et al. 1999). The above points out that careful selection of candidates and interpretation of the results is crucial; too many free parameters would leave doubts about the source of the energy driving the gaseous halos. Based on the above selection, we are confident that halo emission detected in the remaining 11 galaxies of our sample arises from energy input into the ISM from high-mass stars and type II SNe.

   
4.3.2 Measuring techniques

Having ensured that SF dominates the energy input into the disk ISM, the next step in an investigation of a potential connection between halo properties and SF activity in the underlying disk is to quantify the level of energy input and the halo properties.

In earlier studies of halo properties (e.g. Hummel et al. 1991b; Dahlem et al. 1994; Dahlem et al. 1997) we have used z profiles averaged over a broad radial range to quantify the properties of radio halos. This has the advantage of increasing the signal-to-noise ratio compared to a single-pixel profile. At the same time, data are only averaged over regions where emission in the halo has clearly been detected, adapting the measurements to the individual target's geometry.

Ellipsoidal fitting to radio images, as performed by Irwin et al. (1999) makes sense under the assumption that radio halos are engulfing their host galaxies. However, this is not observed in images with sufficient angular resolution. Images that might suggest such behaviour (like, for example, our 1.43 GHz map of NGC1511 in Fig. 4) often suffer from insufficient angular resolution. Instead, with good resolution, a behaviour as described by us earlier (DLG95) is observed in most galaxies: radio halos exist only above the brightest emission regions of the underlying galaxy disks, i.e. the active SF regions. The radial extent of the halos is similar to the radius out to which SF is observed, $r_{\rm SF}$, and thus smaller than that of the entire disks. This is evident in our new 1.43 GHz and 2.45 GHz images of NGC7090 (Fig. 13). Supporting evidence for this result comes from recent H$\alpha$ observations by Rossa & Dettmar (2000). Ellipses do not fit the geometry of the halo plus disk emission properly. We find that the most reliable technique to detect and quantify extraplanar emission is by producing averaged z profiles.

   
4.4 Dependence of halo properties on the level of disk activity?

   
4.4.1 Quantifying the energy input into the disk ISM

Based on radio data of the nearby edge-on galaxies NGC891 and NGC4631, and - with less detailed information - on a few other galaxies, we started investigating whether such a dependence exists (DLG95). As a measure of the energy input into the disk ISM per unit time, $\dot E$, we used the nonthermal radio continuum emission produced by type II SNe. In order to obtain a good measure of the energy density in a given volume within the galaxy disk, the area over which energy input by active SF takes place, $A_{\rm SF}$, was quantified by us. Determining from radial profiles of the radio continuum emission distribution in the disk a cut-off radius of SF processes, $r_{\rm SF}$, we calculated, adopting circular symmetry, $A_{\rm SF}$, as the circular area within the disk of the galaxies over which SF-related energy production occurs, following the simple relation $A_{\rm SF}\ = \pi r_{\rm SF}^2$. $r_{\rm SF}$can be determined equally well from the radial distribution of radio continuum emission in the disk. Data of in total 9 galaxies indicated a trend that those galaxies with the highest energy injection rates, $\dot E/A_{\rm SF}$, per unit time and unit surface area, have the most prominent radio halos (DLG95). Below a certain energy input level no outflows are enabled and galaxies thus do not exhibit extraplanar radio emission. Similar results were reached by Rand (1996) and Meurer et al. (1995, 1997), based on data from other wavebands. A possible link between high energy input rates into the disk ISM and the existence of soft X-ray halo emission is discussed by Ehle et al. (1998) and Dahlem et al. (1998).

The remaining 11 galaxies in the present sample can also be studied for such a dependence. The relevant properties are listed in Table 7. We use as a measure of $r_{\rm SF}$ the beam-deconvolved radial extent of the 1.43 GHz radio continuum emission from our current observations. We limit our studies here to the global energy input as a measure of which we will use the total FIR luminosity $L_{\rm FIR}$, as done by Rossa & Dettmar (2000). Based on the total FIR flux, FIR, following the relation FIR = $1.26\ (2.58\ f_{60} + f_{100}$), we calculate $L_{\rm FIR} = 4 \pi\ D^2\ {\rm FIR}$. $L_{\rm FIR}/A_{\rm SF}$ is the FIR luminosity normalised per unit surface area of the star-forming part of the disk, representing the energy input rate ( $\dot E/A_{\rm SF}$), as defined similarly by us based on radio surface brightnesses (DLG95). This quantity is used as a measure of the global rate of energy injection into the ISM via SF-related processes (stellar winds and type II supernovae), see Col. 7 in Table 7. $z_{\rm0,halo}$, finally, is the exponential scale height of the radio halos from Table 4.

Rossa & Dettmar (2000) have made further progress in another direction, plotting the f₆₀/f₁₀₀ flux ratio vs. the total FIR luminosity (as a measure of $\dot E$) normalised by the disk surface area, $L_{\rm FIR}/D_{25}^2$ (in particular, their Fig. 13), where they find a clear distinction between quiescent and starburst galaxies. All galaxies classified as starbursts by their location in the f₆₀/f₁₀₀ vs. $L_{\rm FIR}/D_{25}^2$ plot (their Fig. 13) have detections of H$\alpha$ emission from extraplanar diffuse ionised gas (eDIG). Compared to DLG95, the FIR luminosity, $L_{\rm FIR}$, substitutes the radio luminosity to represent the level of energy injection, $\dot E$. As a first approximation, Rossa & Dettmar use in their determination of the surface area of the energy input the 25th magnitude isophotal diameter, D₂₅. For the galaxies with wide-spread SF over their disks as used in their sample, this approximation is acceptable. However, in other cases-especially the classic starburst galaxies with circumnuclear activity-the use of D₂₅ can lead to serious errors: systems like, e.g., NGC1808 actively form stars over a much smaller area than their disks out to D₂₅ (e.g., Dahlem et al. 1990). In the present sample NGC3175 is such a case. While its D₂₅ is 5', the diameter of the star-forming part of its disk can be determined (from H$\alpha$ and radio continuum images; see Condon et al. 1996; Ryder & Dopita 1994) very reliably to be only 90'' (7 kpc). Thus, using D₂₅ would lead to an over-estimate of the surface area over which its energy input is distributed, by a factor of 11.1 and thus underestimate the energy density in the disk by the same factor. In these cases one must determine the area over which SF takes place more accurately, by using $r_{\rm SF}$ and $A_{\rm SF}$ instead.

   
4.4.2 The ubiquity of gaseous halos in FIR-warm spirals

Figure 38 corresponds with Figs. 11 and 12 by Rossa & Dettmar (2000). It displays the f₆₀/f₁₀₀ FIR flux ratio (thus a measure of the mean dust temperature) vs. the total FIR luminosity, normalised with the area in which active SF is taking place. In this logarithmic plot all galaxies occupy the upper right-hand quadrant where, according to Rossa & Dettmar (2000) the starburst galaxies fall. Based on our selection criteria the bottom left-hand corner of the plot is empty; there are no quiescent galaxies in the sample. Amongst the galaxies plotted in Fig. 38 a trend is visible that the galaxies with the highest $\dot E/A_{\rm SF}$ values have the highest f₆₀/f₁₀₀ flux ratios and thus mean dust temperatures.

Figure 38: Plot of the f60/f100 FIR flux density ratios vs. the FIR luminosity normalised by the area in which star formation and thus energy input into the ISM takes place, $A_{\rm SF}$. The open squares represent galaxies where halo emission was clearly detected, diamonds denote systems with marginal or no detections.

Figure 39: Plot of the f60/f100 FIR flux density ratios vs. the 1.43 GHz radio luminosity normalised by the area in which star formation and thus energy input into the ISM takes place, $A_{\rm SF}$. The open squares represent galaxies where halo emission was clearly detected, diamonds denote systems with marginal or no detections.

 

 

Table 7: Study of halo scale height vs. energy input level.

Galaxy	${f_{60}}\over{f_{100}}$	$r_{\rm SF}$	$A_{\rm SF}$	FIR	$L_{\rm FIR}$	${L_{\rm FIR}}\over{A_{\rm SF}}$	$z_{\rm0,halo}^{a}$
		(''/kpc)	(103 kpc2)	(10-14 W m-2)	(1043 erg s-1)	(1040 erg s-1 kpc-2)	(kpc)
NGC1055	0.34	236/18.3	1.06	135.85	4.16	3.94	--
NGC1406	0.44	110/ 7.9	0.20	72.74	1.93	9.75	1.66
NGC1421	0.40	145/21.9	1.50	54.43	6.30	4.20	--
NGC1511	0.62	73/ 6.2	0.12	124.81	4.57	38.08	1.76
NGC2748	0.39	103/14.3	0.65	45.54	4.49	6.96	--
NGC3175	0.46	45/ 3.5	0.04	78.02	2.36	62.11	1.62
NGC3437	0.57	96/11.9	0.48	62.77	4.88	10.92	--
NGC3717	0.44	177/23.3	1.71	60.24	5.29	3.09	--
NGC4700	0.57	54/ 6.6	0.14	16.67	1.30	9.35	3.06
NGC7090	0.33	131/ 7.4	0.17	41.76	0.68	3.93	1.77
NGC7462	0.49	103/ 7.5	0.18	18.07	4.93	27.54	1.82
NGC1569	0.96	72/0.77	0.00186	207.20	0.12	64.50	--

Note to Table 7: ^a) 1.425-1.49 GHz measurements only; average values from Table 4.

The new result of our investigation is that in 6 out of 11 objects radio halo emission has been detected (open squares). There is a clear trend that halos were detected in those galaxies with the highest $\dot E/A_{\rm SF}$ and f₆₀/f₁₀₀ values, with the notable exception of NGC3437, which was discussed above. We have selected highly inclined galaxies only for technical reasons. The fact that most, if not all FIR-warm edge-on galaxies have radio halos should apply to galaxies with any inclination angle. We just need to develop tools to find them in more face-on systems.

We have produced the same kind of plot as Fig. 38 based on the total 1.43 GHz radio continuum flux density, as listed in Table 3, which is presented in Fig. 39. The total 1.43 GHz radio luminosity was calculated using the equation $L_{1.43}\ = 4\,\pi\ D^2\ S_{1.43}$, neglecting the term $(1+z)^{1+\alpha}$, because it is not relevant for the low-redshift galaxies studied here (Condon et al. 1990). Because of the strong radio-FIR correlation the two plots look almost identical, although the positions of individual galaxies can shift with respect to their location in Fig. 38. This similarity of the two plots-and thus relations between luminosity and dust temperature-makes our present study and the results by Rossa & Dettmar (2000) comparable to our earlier investigations (DLG95). As in Fig. 38, the data points in Fig. 39 also indicate a trend of the galaxies with the highest $\dot E/A_{\rm SF}$ values having the highest mean dust temperatures.

A second important result is that all physically small galaxies (with $D_{25} \leq\ 20$ kpc; in the present sample NGC1511, NGC4700, NGC7090 and NGC7462) have prominent radio halos. Their total mass being low, it appears to be easier for CR electrons to escape from the thin disk than in galaxies with higher total masses, $M_{\rm tot}$. Even NGC7090, with a moderate mean dust temperature and also a correspondingly moderate energy injection rate ( $L_{\rm FIR}/A_{\rm SF}$; note that NGC1055 and NGC7090 have almost equal values, see Table 7), can produce a radio halo. Radio halos are visible, because these galaxies are no dwarfs (in which case they might be too light to retain their magnetic fields so that CRs might escape almost loss-free and thereby remain invisible), but intermediate-mass systems.

We note here that the simplifying assumption has been made that all energy contained in CR electrons emitting synchrotron radiation originally arises from the galaxy disks. Lacking images showing details, such an assumption must be made, without any distinction as to where the radio continuum emission comes from. The same assumption is made for the FIR data too (not only by us, but also by Rossa & Dettmar 2000 and other investigators).

Based on a larger sample, Irwin et al. (1999) did not find a connection between the properties of gaseous halos and the global level of underlying SF activity, using radio continuum images. However, these authors did not distinguish between different object classes contained in their sample due to the small number of galaxies in total. From their sample, NGC3735 and NGC4388 should be excluded, because they host Sy-2 nuclei (NED). The existence of a radio halo in NGC3432, despite its low energy injection rate, can be explained because it is a magellanic irregular with low total mass and thus shallow gravitational potential, similar to the small galaxies in our sample. In addition, NGC3432 is closely interacting and should therefore be removed from the sample for studies of the dependence of halo properties on the level of underlying SF activity in the galaxy disk. NGC5433 and IC562 from the sample by Irwin et al. (1999) should be excluded, as we did above with NGC5073 and NGC7541, because their emission distribution is not resolved by the data. Once this target selection is applied, we do see a trend in the data by Irwin et al. (1999) suggesting that the galaxies with the highest $\dot E/A_{\rm SF}$ values have halos, while those with lower energy input levels do not always have halos. Therefore, there is no contradiction in the data by these authors to our hypothesis from the paper by DLG95. Instead, their data support our claim, as do our new results presented here, that late-type spiral galaxies with warm dust do have gaseous halos and that those with the most active SF tend to have the most prominent halos.

   
4.4.3 Why is there no direct relationship between $\mathsfsl{z}_\mathsf{0,halo}$ and $\mathsfsl{\dot E/A}_\mathsf {SF}$?

However, trying to go one step further, we find that there is clearly no direct quantitative relationship between the halo scale height, $z_{\rm0,halo}$, and the normalised energy input, $\dot E/A_{\rm SF}$, as listed in Table 7.

In our earlier sample (DLG95) we presented only L_* galaxies, i.e. systems near the "knee'' of the galaxy luminosity function, with total masses somewhere on the order of $10^{11}\ M_\odot$. There, we found a trend that galaxies with the highest SF rates in their disks have the most prominent halos and that the halos are brightest above the most actively star-forming regions.

The present sample, as indicated above, contains a number of physically small galaxies as well as L_* galaxies. This implies that, compared to our earlier study (DLG95), an additional free parameter has entered the equation, namely the different resistence that particles meet when expelled from their birth sites in the disks.

We have therefore tried to normalise the energy input rate not only by the area over which it is distributed, but also by the gravitational potential of the galaxy as measured by the total mass. Also for this quantity we have found no convincing correlation with $z_{\rm0,halo}$. This implies that yet more, or other, factors affect the propagation of CRs out of galaxy disks. In particular, the energy losses that CR electrons undergo on their way out of the disk influence the properties of the observed radio halos: Although predicting different kinds of behaviour, both static and dynamic models of CR radio halos (Lerche & Schlickeiser 1981a-c; Werner 1988) predict a dependence of the extent of radio halos on the mean lifetime of the CR electrons. In case of pure diffusive CR propagation the dependence is directly proportional to the diffusion index of the CRs. The influence of convection is expected to increase with increasing energy input. However, at the same time inverse Compton losses become more important with increasing energy input too. This is the reason why no direct dependence is found between the measured scale heights and the level of energy input in the underlying disks.

Significant energy losses of the CR electrons leaving the disk are in agreement with the observed slight steepening of the radio spectral indices (Sect. 3.3).

   
4.4.4 $\mathsfsl{r}_\mathsf{SF}$ vs. radial halo extent

Based on images with sufficient spatial resolution a direct morphological comparison can be made, as done by us earlier (DLG95), of the radial extent of the radio halo with respect to the radial extent of the actively star-forming part of the disk, $r_{\rm SF}$. We had found in our previous sample that the radio halo emission breaks off radially near the point where the surface brightness in the disk drops rapidly, i.e. $r_{\rm SF}$. This implies that halo emission is observed only above the most actively star-forming parts of the galaxy disks. In the present sample, the ATCA data have the highest angular resolution. The effect is visible most clearly in NGC7090, and also-though to a lesser degree-in NGC7462 (here especially at 2.45 GHz, where the angular resolution is highest). Higher resolution is required to study the same effect in the galaxies observed with the VLA D array, especially in cases like NGC4700 (cf. Fig. 11). In the case of NGC3175 the data by Condon et al. (1996) suggest the same behaviour. The extraplanar radio emission is restricted to the radial regime of the central starburst. More details on this will be presented elsewhere.

Despite the relatively good spatial resolution of our data, NGC1511, with its very smooth emission distribution, shows little of this effect. It comes closest to the ellipsoidal emission distribution that might be expected in case of purely diffusive particle propagation.