Figure 8a
shows the plot of SBIR versus isophotal diameter (D(Kpc))
for the
30 Kpc.
The most plausible explanation for this phenomenon is that bursts
can be seen
If this simple model is correct, the largest values of LIR
for the smallest galaxies
(Log(L IR) ~ 10.6) would give an approximate upper limit
for the strength of a burst.
In addition, you would expect that the upper limit for the SB
IR of galaxies plotted in
figures 8a and 8b would fall off as D(Kpc)-2, provided the
upper limit for burst strength
is not strong function of D(Kpc).
Confirmation that our simple model is indeed correct is shown by
the curves in figures 8a and 8b.
These curves connect points that have an infrared luminosity
Log(LIR ) = 10.6. As predicted, the curves form an upper
bound to the distribution of
the data points in the two figures. Hence, the only reason that we do
not see bursts in galaxies with
diameter > 30.0 Kpc is the fact that:
b)it becomes progressively
more difficult to see the burst against the
steady-state infrared emission of
the underlying parent galaxy as the
galaxy becomes larger and more massive.
the SN production rates should increase with
increasing galaxy size and mass. This is true whether or
not a galaxy is undergoing a burst in its star
formation rate.
rates produced by the bursts.
Hence, it isn’t surprising that we do not see large spirals preferentially producing SNII but not SNIa, even though they may be experiencing bursts in their absolute star formation that are comparable in size to those seen in the smaller galaxies.
ii) The effect of bursts on
the (B-V)To colours and the H-alpha
equivalent widths.
Figure 9a shows the SBIR for both Burst and Non-Burst spirals in the Base sample plotted against the galaxy’s (B-V)oT colour (de Vaucouleurs et al. 1991).Figure 9b is the corresponding plot for the SNII and SN Ia galaxies in the SN sample. These figures clearly show that there are very few Burst galaxies with (B-V) o T colours that are redder than 0.60, while Non-Burst galaxies can have (B-V)o T colours all to way up to a value of 0.8. The upper limit for (B-V) oT dramatically shifts from 0.8 to 0.6 at SBIR ~ 30 – 35, showing that enhanced star formation activity in the burst spirals is large enough to have a significant impact on the overall integrated (B-V)oT colours of the underlying parent galaxy.
Another sensitive indicator of the presence of bursts in spirals is the H-alpha equivalent widths. Kennicutt (1978) found that the H-alpha equivalent widths of many interacting spirals are enhanced compared to non-interacting spirals of the same (B-V)T colour. Models developed by Kennicutt (1987) and Belfort (1987) show that the enhanced H-alpha equivalent widths in the interacting spirals can best be explained by short duration (~ few x 107 years) bursts of star formation superimposed upon the underlying galaxies.
The galaxies in Kennicutt’s sample are subdivided into two main
groups,
Figure 10 clearly shows that the Burst and Near-Burst spirals for
both the
In order to gauge the level of enhancement in star formation in burst
spirals,
In what appears to be a contradiction, the models seem to indicate that there is a group of red (i.e. (B-V)To > 0.60) Non-Burst spirals that are experiencing enhanced current to integrated star formation rates. Interestingly, three out of f our of the most extreme examples of this group (NGC 3521, NGC 5055 and NGC 7479) are large spirals with D25 > 30 Kpc. This adds support to our earlier assertion that it possible for bursts to exist in large spirals but go undetected because they do not standout against the background galaxy.
iv) The Gas Problem
Figure 11 is a plot of the logarithm of the infrared surface brightness (log (SB IR)) versus the logarithm of the total gas mass (HI + H2 ) surface density (log (SD(HI + H2 )), for all the Sbc-Sdm NGC/IC spirals in the sample of Young et al.1996. Different symbols have been used to sub-divide the galaxies into Non-Burst spirals, Burst spirals and mergers.
Figure 11 shows that, for non-merging spirals, SBIR is proportional to (total gas mass surface density) n with “n” changing from roughly two for the low infrared surface brightness galaxies to one (or less) for galaxies with high infrared surface brightness. In addition, it is evident from figure 11 that the Burst spirals have the highest total gas mass surface densities amongst the non-merger galaxies. (Note: When we look at the two merger galaxies in figure 11, we see that NGC 3310, appears to continue the trend set by the non-merger galaxies while NGC 1614 appears to have much higher SBIR than expected for its total gas mass surface densities.) Hence, an Sbc-Sdm spiral galaxy must not only be small (D 25 < 30 Kpc) to have a detectable burst, it must also have a high total gas mass surface density as well.
This latter result seems to put the Burst model into question, since the model would require Non-Burst galaxies with low total gas mass surface densities to evolve into Burst galaxies with high total gas mass surface densities and back again. This would mean that the galaxies would have to experience an infusion of fresh gas from outside prior to their bursts. In addition, they would have to consume this additional gas in a time scale that is comparable to the length of the epoch in which Burst galaxies produce SN II at a much higher rate than they produce SN Ia i.e. 0.85 – 1.35 x 10 8 years.
In order to gauge the magnitude
of this problem, we need to determine the
amount of gas that Burst spirals must absorb and consume during the
epoch of enhanced SNII production.
Figures 12a
, 12b
and 12c
show the respective log-log plots
for the molecular hydrogen mass (MH2), atomic hydrogen
mass (MHI) and total gas mass (Mgas), versus isophotal
diameter (D 25 (Kpc)) for the Sbc – Sdm galaxies in the
sample of Young et al. 1996. In each figure, least squares lines of
best fit have been plotted for both Burst and Non-Burst galaxies. These
lines of best fit show that the M H2
If we arbitrarily choose a diameter of 20 Kpc (i.e. Log (D(Kpc)) = 1.30) as our benchmark, we can see from the least squares lines of best fit in figures 12a – 12c that the M H2 of Bursts galaxies is higher than that of Non-Bursts by ~ 0.55 in the log (9.70 versus 9.15, respectively), the MHI of Bursts is higher than that of Non-Bursts by ~ 0.15 in the log (9.70 versus 9.55, respectively), and M gas of Bursts is higher than that of Non-Bursts by ~ 0.30 in the log (10.00 versus 9.70, respectively). These values can be used to give rough estimates of the additional gas mass that, according to the Burst model,would have to be absorbed by Burst spirals.
The data in Figures 12a –
c shows that for spirals with an isophotal diameter of 20 Kpc, the average
Burst galaxy has an additional ~ 3.6 x 10 9 MO
of H2 gas, ~ 1.5 x
10 9 M O of HI gas, and ~ 5 x 10 9
M O of total gas mass, compared to the
average Non-Burst galaxy. In order to place these figures in perspective,
it should be noted that our own
Galaxy contains
~ 4 x 109 MO of H2 gas and
~ 5 x 10 9 MO of HI gas (Mihalas and Binney1981).
Hence, it would appear that the Burst model requires that Burst galaxies
absorb and consume H2 gas masses comparable to
those of our own Galaxy, all within a period of
~ 0.85 – 1.35 x 108 years.
Since it is the molecular hydrogen
gas, in the form of giant molecular
clouds, which supplies the bulk of the fuel for massive star formation
(Knapp 1990)and since the length
of the epoch of enhanced SNII production is ~ 0.85 – 1.35 x 10
8 years
then it would require an average absolute star formation rate for
the Burst spirals of approximately
27 – 42 MO per year in order to consume all the molecular
hydrogen infused over the lifetime
of enhanced SNII production. This compares with measured average absolute
star formation rate of ~ 7 MO
per year obtained by Young et al. 1996 from the observed H-alpha
luminosities of these galaxies
(note: The H-alpha luminosities of Young et al. have be converted
to HO = 75 and they have been corrected for a uniform
extinction in front of the HII
regions (AH
a) of 1.1 magnitudes, as suggested by Kennicutt
and Kent 1983).
Hence, it appears that the Bursts model would require burst spirals to absorb and consume H2 gas at a rate that is 4 – 7 times higher than the observed rate. Fortunately, there are three alternative explanations that might enable us to get around the troubling gas consumption problem and the need for a gas infusion.
Firstly, it is very unlikely
that the burst process will be 100 % efficient in
consuming all of the molecular hydrogen that is involved in the
burst. A more likely outcome, is one in which a fraction (f) of the
molecular mass (i.e. f MH2 ) is converted
into stars by the burst, while the remainder is converted into
atomic hydrogen (i.e.(1-f)M H2 ) by the energy released by
the burst.
In this case, the observed absolute star formation rates can be reconciled with those predicted by the Burst model if 16 – 26% of the molecular hydrogen gas mass that is absorbed by a burst galaxy be converted into stars i.e. f = 0.16 – 0.26. This assumes, of course, that the pre-existing gas within the galaxy is not involved in the burst. In the more likely situation where the pre-existing H2 gas is also involved in the burst, the values of “f” would even smaller. The problem with such low “f” values is that virtually all of the infalling H2 gas is converted into HI ( ~ 3.6 x 109 MO) and so there should be a population of post-burst spirals with significantly enhanced HI gas masses compared to pre-burst galaxies of similar isophotal diameters. Unfortunately, there are no obvious group of galaxies fitting this description in figure 12b. Hence, the efficiency with which the in falling H2 gas is converted into stars cannot be used to completely eliminate the gas problem in Burst spirals.
Models developed by Elmegreen (1993) provide a second possible solution for the gas problem. His models show that large regions of spiral galaxy disks can spontaneously convert from HI to H2 following an interaction or other event that triggers mass accretion or an increase in the mass surface density. Hence, it is possible that a part of the H 2 increase we observe in Burst spirals could also come from this effect. However, spontaneous wide spread conversion of HI into H 2 in Burst spirals could not possibly be responsible for the majority of the additional H2 gas (~ 3.6 x 109 MO in spirals with isophotal diameters of 20 Kpc) as it would require that almost all of the HI gas in the Burst spirals be converted into H 2. The data displayed in figures 12a – c does not support this result.
A third alternative solution to the gas problem in Bursts comes from the fact that the majority (~ 70 %) of the apparent increase in gas mass in the Burst spirals is in the form of H 2 and not HI. Thus, it is possible that part of the apparent increase in H 2 gas mass in Burst galaxies may not be real but simply the result of an increase in the CO ¬> H2 conversion ratio caused by the onset of the burst.
Young et al. (1996) derive their H2 gas masses from their CO fluxes by applying the conversion factor (X) for the Galaxy (Bloemen et al. 1986):
to all of their sample galaxies. This value of the conversion factor leads to a H2 masses in solar units given by:
where S(CO) is the galaxy’s global CO flux.
Theoretical models indicate that you would expect that the conversion factor X should vary as:
where 
There is strong evidence that in galaxies where there is significantly enhanced star formation, the molecular clouds are exposed to much more intense radiation fields (Maloney 1990). The enhanced radiation fields increase the gas temperature in the molecular clouds, resulting in a decrease in the CO ¬ > H2 conversion ratio X. As a result, it possible that the H2 masses are overestimated for galaxies which are experiencing significant bursts in the level of their star formation.
Thus, the presence of bursts
in spirals galaxies provides a possible solution to
the gas mass consumption problem by reducing the amount of gas
which must be consumed over the
epoch of enhanced SN II production. Indeed, it is possible to
completely eliminate the apparent excess of H2 in Burst
galaxies by reducing the CO ¬
>
H2 conversion ratio X by a factor of
~ 3.5, compared to the Galaxy.
(Note: we designate the amount by which X is reduced compared to
the value of X in the Galaxy
as “
DX” e.g. in this case
DX =
0.29). Of course, since we do not
know for certain if and by how X is reduced, all we can say is
that, provided 1.00 >
DX >
0.29, any combination of “f” and “
DX” which produces an
f
DX <
0.16 – 0.26 (e.g.
f = 0.5 and
DX =0.3)
will produce agreement between
the observed absolute star formation rates in the Burst galaxies
(~ 7 M per year) and the absolute
star formation rates implied by the Burst model.
If the CO ¬ > H2 conversion ratio X for Burst spirals is less than ~ 3.5 times smaller than that of non-Burst spirals then the Bursts spirals must absorb H 2 gas from their surrounding and convert a fraction (f) of this gas into stars. Unfortunately, there is no way to determine the amount of gas that is absorbed by the Burst spirals until we can quantify DX, f, and the amount of pre-existing gas within the galaxies that becomes involved in a burst . The only constraints we can place upon the H2 gas consumed by spirals during a burst is a lower limit upon the total H 2 gas (internal + infused) from current star formation rates determined from their H-alpha luminosities.
v) Gas consumption rates implied
by the rates of current star formation
Figures 13a shows the plot of the absolute current star formation rates (CSFR) versus isophotal diameter (D25) for all of the Sbc-Sdm NGC/IC galaxies in the sample of Young et al. 1996. The CSFR in figure 13a have been converted to H O = 75 and they have been corrected for a uniform extinction in front of the HII regions (A H a) of 1.1 magnitude, as suggested by Kennicutt and Kent 1983.
For comparison purposes, figure 13a is replotted in
figure 13b
, taking into account our
findings in section III of this paper that that the
H-alpha
extinction found in
The current star formation rates for stars with masses between 0.1 and 100 MO have been calculated using the formula:
where L(H -alpha ) is the galaxy’s H-alpha luminosity in units of solar luminosities (Young et al. 1996). This formula assumes an initial mass function phi (m) that is proportional to m-1.4 for 0.1 < m < 1 MO and m-2.5 for 1 < m < 100 MO (Kennicutt 1983).
Figures 13a and 13b shows that while the absolute current star formation rate for Non-Burst spirals increases slowly with increasing galactic size, the star formation rates for Mergers, Burst spirals and Near Burst spirals show a completely different trend, increasing almost linearly with D25 (Kpc). These figures also show that the average absolute current star formation rate for the Burst spirals is ~ 7 MO per year.
If the Burst galaxies maintain this rate over the life-time of the enhanced SNII production, lasting for ~ 0.85 – 1.35 x 108 years, they will consume at least 6.0 – 9.5 x 108 MO of H 2 gas. Obviously, this H2 gas mass is only a lower limit to the actual amount of total H2 gas (internal + infused) consumed by the Burst galaxies as only a fraction “f” of H 2 gas absorbed is turned into stars. If, for example, we assume that f = 0.5 then the amount H 2 gas consumed by the Burst spirals during their bursts could be as high as ~ 1.2 – 2 x 109 MO.
Suppose that, for argument sake, a third the H2 gas consumed by the Burst spirals comes from outside the galaxy (i.e. ~ 4.0 – 7.0 x 10 8 MO ), then the most likely source for such a large amount of H2 gas would be gas–rich dwarf irregular galaxies that are in orbit about these galaxies. The gas-rich Sm spirals and irregular galaxies are the best source for the H2 gas because:
near complete distance-limited sample of
nearby (recession velocity <
500 km/sec) galaxies, Sm spirals (T = 9)
andirregulars (T=10)
make up almost 2/3 (95 out of the 146 or 65 %) of all
galaxies in their sample.
iv) What causes the bursts?
One possible cause for bursts in spirals is tidal interaction with close companions (Huchra 1977, Larson and Tinsley 1978 and Kennicutt et al. 1987). In order to gauge how important this mechanism is for producing bursts, we have conducted a preliminary search around each of the SN sample galaxies to look for close companions.
The commercial software program
Hypersky (1999) was used to search
the RC3 catalogue (de Vaucouleurs 1991) for close companions. A
SN sample spiral was designated to have a close companion if there was
another galaxy in the RC3 catalogue
that had a projected separation from the SN galaxy of
< 0.2
Mpc (H o = 75 km/sec/Mpc ) and a recession velocity difference
<
300 km/sec. If no such galaxy
exists then the SN sample galaxy was designated as not having
a close companion.
This means that we have limited the search for companions to galaxies that are intrinsically as bright or brighter than the LMC, which has an mB = 14.7 at distance of 33 Mpc. Interestingly, the our own galaxy would just miss out on being classified as a spiral with a close companion [the LMC is located at a distance of 0.05 Mpc] since the LMC would probably not make it into the RC3 catalogue if it were placed at a distance of 33 Mpc, because of its size.
(Note: No attempt was made to search for close companion galaxies around SN sample spirals in the Virgo clusters because the high peculiar velocities of these galaxies significantly increases the probability that any close companion is an interloper.)
Figure 14a
is a plot of SBIR versus isophotal diameter (D
25 ), showing the SNII
sample galaxies without close companions. Figure
14b
is the corresponding plot that
shows the SNII sample galaxies with close companions. A curve
has been drawn in both these figures marking the location galaxies
with log(L IR) = 10.2 (LO). These two
figures clearly show that, for isophotal diameters below 25 – 30
Kpc, SNII galaxies with close
companions have systematically higher SBIR than SNII galaxies
of comparable isophotal diameter
without close companions. Note: the data point
for the Galaxy is plotted in figure 14b for comparison purposes, using
values of D25
= 26 Kpc and Log(LIR) =
9.8 (LO) (Young 1990), which corresponds
to an
SBIR = 8.3 (in units of 106 L O
Kpc -2).
Figures 15a and 15b show the corresponding plots for galaxies in the SNIa sample. While the SNIa sample galaxies without close companions appear to show the same trend as SNII counterparts, there are not enough SNIa sample galaxies with close companions to make a valid comparison.
In essence, figures 14a and 14b are telling us that SNII galaxies with close companions appear to have systematically higher infrared luminosities (LIR ) than SNII galaxies without close companions. This is confirmed in figures 16a and 16b , which show the respective frequency distributions of Log(L IR) for those SNII sample galaxies with companions and those without. If a two-tailed Wilcox rank sum test is carried out on the two data distributions, it shows that the probability of obtaining a difference as great as or greater than that found between the means of the two samples is < 0.01, indicating that is highly unlikely that the difference between the two data distributions is the result of chance. Hence, the data for SNII galaxies is consistent with the idea that:
a) for galaxies with isophotal diameters
< 25 – 30 Kpc, if a galaxy’s current star
formation rate is enhanced (i.e. it
has an enhanced LIR) then it has a close companion
(< 0.20 Mpc). Note: The data does not support the converse,
hence, it is possible for a galaxy
to have a close companion but not have
an enhanced current star formation rate.
The Galaxy is a good example of
this possibility.
b) it is easier to distinguish
bursts (i.e. enhancements in the galaxies LIR) in
smaller galaxies (by their enhanced SBIR)
because the bursts are seen
against a lower overall level of steady-state star formation rate.
Our results are consistent with the more comprehensive study of Barton et al. (2000). The authors of this paper have selected a sample of 502 close galaxy pairs and N-tuples from the Cfa2 redshift survey that are in the early stages of a merger. All of the galaxy pairs are separated by < 0.055 h-1 Mpc. Barton et al. (2000) found that the EQW(H-alpha) and the strength of other emission lines strongly anti-correlated with pair spatial separation and velocity separation. Their data supports a simple picture in which a close pass between two disk galaxies initiates a burst of star formation in the pair, dramatically increasing their EQW(H-alpha) emission. Subsequently, the EQW(H-alpha) emission decreases as the pair separation increases, accounting for the anti-correlation which they observe. They also find that their data is compatible with starburst models and orbit models, so long as the starburst lasts longer than ~ 108 years, and the delay between the close pass and the initiation of the starburst is less than a few times 10 7 years.
Our infrared data can be compared with the EQW(H-alpha) data of Barton et al. (2000) by plotting L IR and SBIR for each of the SN sample spirals against the distance to their companion galaxy with the smallest projected separation on the sky. The companion galaxies with the smallest projected separations were identified by searching through all of the galaxies in the RC3 catalogue with published total apparent B magnitudes (m B) and recession velocities (de Vaucouleurs et al 1991). The search for companions was limited to those galaxies:
a) which are bright enough to
be seen over the full volume of the SN sample i.e. we have chosen
to include only those
companion galaxies with mB brighter
than 15.0, when placed at a distance of
33 Mpc (i.e. Vo(3K) = 2,500 km/sec
for Ho = 75 km/sec/Mpc).
b) with recession velocity differences
of <
300 km/sec, when the projected
separations are
< 0.20 Mpc (Chengalur et al.
1996, Zarinsky et al. 1993, 1997).
c) with recession velocity differences of < 150 km/sec, when the projected separations are > 0.20 Mpc.
The limitations in recession velocity difference have been chosen to minimize the likelihood of sample being contaminated by interloper galaxies. The choice of 150 km/sec for galaxy pairs with projected separations > 0.20 Mpc, is a compromise between the low spread in velocity differences observed for isolated pairs ( ~ 30 km/sec) and the much higher spread in velocity differences observed for pairs in galaxy groups ( ~ 300 km/sec) (Chengalur et al. 1996). It is possible that our chosen velocity difference cut-off for galaxy pairs (with projected separations > 0.20 Mpc) will exclude a few genuine galaxies with projected separations lying between 0.20 Mpc and the quoted minium separation. However, this source of error does not critically affect our analysis as we are really only interested incomparing SN sample galaxies with close companions with those that do not.
Figure 17a shows LIR (in units of 10 9 LO ) for each of the SNII sample galaxies plotted against the projected separation to their nearest companion galaxy. Figure 17b is the corresponding plot for the SNIa sample spirals. In like manner, figure 18a shows SBIR for each of the SNII sample galaxies plotted against the projected separation to their nearest companion galaxy, while figure 18b is the corresponding plot for the SNIa sample spirals.
It is immediately obvious from
a comparison of these four plots that: