Dwarf irregular galaxies are like the outer parts of spiral galaxies in terms of gas surface density, SFR, and gas consumption time. Tiny dIrrs have extended exponential disks as well. For example, Saha et al (2010) traced the Large Magellanic Cloud (LMC) to 12 RD, an effective surface brightness of 34 mag arcsec−2 in I, and Sanna et al (2010) found stars in IC 10 to ∼ 10 RD. Bellazzini et al (2014) detected stars associated with Sextans A and Sextans B to 6 RD, and Hunter et al. (2011) measured surface brightness profiles in four nearby dIrrs and one BCD to 29.5 mag arcsec−2 in V, corresponding to 3−8 RD. These extended stellar disks represent extreme galactic environments for star formation and are potentially sensitive probes of galaxy evolutionary processes, and yet they are relatively unexplored. In this Section we examine what is known about outer disks of dIrr galaxies.
The H i gas often dominates the stellar component of dIrr galaxies, both in extent and mass. How much further the gas extends compared to the stars was demonstrated by Krumm and Burstein (1984) for DDO 154 where the H i was traced to 8 R25 at a column density of 2 × 1019 atoms cm−2 (0.22 M⊙ pc−2). In the LITTLE THINGS sample of 41 nearby (< 10.3 Mpc), relatively isolated dIrrs (Hunter et al 2012), most systems have gas extending to 2−4 R25 or 3−7 RD at that same (face-on) column density. Some spiral galaxies also have extended H i; Portas (2010) found that the Sbc galaxy NGC 765, for example, has gas extending to 4 R25. Large holes (up to 2.3 kpc diameter) are also sometimes found in the gas beyond 2 RD (Dopita et al (1985), R.N. Pokhrel, in preparation).
In most dIrrs, the galaxy is gas-dominated and becomes increasingly gas-rich with radius (Fig. 3). This implies a decreasing large-scale star formation efficiency (Leroy et al 2008, Bigiel et al 2010). The lack of sharp transitions in the star-to-gas ratio, including at breaks in the optical exponential surface brightness profiles, suggests that the factors dominating the drop in star formation with radius are changing relatively steadily.
 |
Figure 3. Azimuthally averaged stellar mass to gas mass ratios as a function of radius normalized to the disk scale length (top) and radius at which the V-band surface brightness profile changes slope RBr (bottom). These galaxies are from the LITTLE THINGS sample with stellar mass profiles determined by Zhang et al (2012) and gas mass profiles from Hunter et al. (2012). |
The gas surface density drops off with radius usually in a non-exponential fashion. In Sect. 2−7, we have approximated the radial gas profiles of spiral galaxies as exponentials. However, especially in dIrrs, the gas profiles are rarely pure exponentials, and since dIrrs are gas-dominated, the shape of the gas profile is crucial. Note, however, that in dIrrs, the radial stellar profiles are usually exponential in shape. In a sub-sample of the THINGS spirals (Walter et al 2008), Portas (2010) found that the gas is approximately constant at 5−10 × 1020 atoms cm−2 and then drops off rapidly. A Sersic function fits the profiles with indices of n = 0.14−0.22. For comparison, an exponential disk has an n of 1.0. In five THINGS dIrrs the gas density dropped more shallowly with radius, and the distribution of n peaked around 0.3. For the LITTLE THINGS sample of dwarfs, the shape of the H i radial profiles varied from galaxy to galaxy, and n varied from 0.2 to 1.65 with most having values 0.2−0.8. The lack of correlations between the H i profile index n and characteristics of the stellar disk suggest that the role of the gas distribution in determining the stellar disk properties is complex.
Zhang et al (2012) performed spectral energy distribution fitting to azimuthally-averaged surface photometry of the LITTLE THINGS galaxies. The fitting included up to 11 passbands from the FUV to the NIR. From these fits they constructed SFRs as a function of radius over three broad timescales: 100 Myr, 1 Gyr, and galaxy lifetime. Zhang et al found that the bulk star formation activity has been shrinking with radius over the lifetime of dwarf galaxies, and they adopted the term “outside-in” disk growth. Although Zhang et al found that “outside-in” disk growth applied primarily to dIrrs with baryonic masses < 108 M⊙, Gallart et al (2008) and Meschin et al (2014) found the same phenomenon in the LMC, a more massive irregular galaxy. Similarly, Pan et al (2015) suggested from colour profiles that the same process is occurring in a large sample of Sloan Digital Sky Survey galaxies with stellar masses up to 1010 M⊙. This outside-in disk growth is in contrast to the inside-out disk growth identified in spirals (White and Frenk 1991, Mo et al 1998, Muñoz-Mateos et al 2007, Williams et al 2009, but see Ruiz-Lara et al 2016).
Hunter et al (2011) carried out an ultra-deep imaging program on four nearby dIrrs and one BCD. They measured surface photometry in this sample to 29.5 mag arcsec−2 in V, and also obtained deep B images of three of the galaxies and deep FUV and NUV images with the Galaxy Evolution Explorer (GALEX, Martin et al 2005). Fig. 4 shows the V-band image and photometry of DDO 133, illustrating what they found. What does a surface brightness of 29.5 mag arcsec−2 mean? In DDO 133, that is a factor of ∼ 160 down in brightness from the centre. A 1 kpc-wide annulus at 29.5 mag arcsec−2 corresponds to a SFR of 0.0004 M⊙ yr−1, assuming a mass-to-light ratio from the B − V colour and a constant SFR for 12 Gyr. This is roughly seven Orion nebulae every 10 Myr.
 |
Figure 4. Left: V-band image of DDO 133 from Hunter et al (2011). The white ellipse marks the extent of the galaxy measured to 29.5 mag arcsec−2. The white contours trace column densities of 5, 30, 100, 300, 500, 1000, and 3000 × 1018 atoms cm 212;2 in H i (Hunter et al. 2012). Top right: Surface photometry in V, FUV, and B − V as a function of radius normalized to the disk scale length RD. Bottom right: V-band surface photometry of all five galaxies from Hunter et al (2011). IZw115 is a BCD; the rest are dIrrs. |
In their five dwarfs, Hunter et al (2011) found that the stellar surface brightnesses in V and FUV continue exponentially as far as could be measured. Furthermore, the stellar disk profiles are exponential and extraordinarily regular in spite of the fact that dIrr galaxies are clumpy in gas and SFR and star formation is sporadic. Saha et al (2010) found the same thing for the LMC, and Bellazzini et al (2014), for Sextans B. However, Bellazzini et al. also found that, by contrast, Sextans A has a very complex surface brightness profile and suggested that that is the consequence of past outside perturbations, assuming that a regular profile is “normal” for an isolated galaxy.
The deep FUV surface photometry of Hunter et al (2011) also shows that there is a continuity of star formation with radius. The Toomre (1964) model, in which star formation is driven by two-dimensional gravitational instabilities in the gas, predicts a precipitous end to star formation where the gas surface density drops below a critical level. Nevertheless, these data show that young stars extend into the realm where the gas is a few percent of the critical gas density and should be stable against spontaneous gravitational collapse (Kennicutt 1989). Models suggest that dIrrs need to be treated as three-dimensional systems, in which case the Q parameter is not a good measure of total stability. Also, the dynamical time at the mid-plane density is more important than the growth time of a two-dimensional instability, which is more closely related to spiral arms than star formation (Elmegreen 2015, Elmegreen and Hunter 2015).
The presence of FUV emission in outer disks poses a stringent test of star formation models by extending measures of star formation activity to the regime of low gas densities. How low can the gas density get and still have star formation? H ii regions have been found in the far-outer disks of spirals (Ferguson et al 1998), and GALEX has found FUV-bright regions out to 2−3 times the optical radius of the spiral (Gil de Paz et al 2005, Thilker et al 2007). Bush et al (2008) proposed that these FUV regions could be due to spiral density waves from the inner disk propagating into the outer disk and raising local gas regions above a threshold for star formation. In fact, Barnes et al (2012) found evidence for greater instability in outer disk spirals compared to inner disk spirals in eight nearby spiral galaxies. Dwarf irregular galaxies, however, do not have spiral density waves, and neither do the far-outer parts of the galaxies observed by Watkins et al (2016), so the problem still remains of how stars form in or get scattered to extreme outer disks.
Recently, GALEX images have been used to identify FUV-bright knots in the outer disks of dIrrs in order to determine how far-out young star clusters are formed in situ and the nature of the star clusters found there. Hunter et al (2016a) identified the furthest-out FUV knot of emission in the LITTLE THINGS galaxies, and found knots at radii of 1−8 RD (see Fig. 5). Most of these outermost regions are found intermittently where the H i surface density is ∼ 2 M⊙ pc−2, although both the H i and dispersed old stars go out much further (also true of some spiral galaxies; e.g., Grossi et al 2011). In a sample of 11 of the LITTLE THINGS dwarfs within 3.6 Mpc, Melena et al (2009) identified all of the FUV knots and modelled their UV, optical, and NIR colours to determine masses and ages. They found no radial gradients in region masses and ages (see Fig. 6 for an example), even beyond the realm of Hα emission, although there is an exponential decrease in the luminosity density and number density of the regions with radius. In other words, young objects in outer disks cover the same range of masses and ages as inner disk star clusters.
 |
Figure 5. Left: Histogram of the distance from the centre to the furthest knot of FUV emission in the LITTLE THINGS dIrrs relative to the disk scale length RD (Hunter et al 2016a). Right: Distance from the galaxy centre to the FUV knot vs average H i surface density at the radius of the knot. The ΣHI have been corrected for a scaling error as described in Hunter et al (2016b). |
 |
Figure 6. Plots of mass vs. age, mass vs. galactocentric radius, and age vs. radius for WLM, one of the galaxies from Fig. 3 of Melena et al (2009). The radius corresponding to the extent of Hα is marked with a vertical dashed red line, and the regions outside the Hα extent are in red. The horizontal dashed line in the left panel is the mass limit for completeness to an age of 500 Myr. The slanted dashed line is a fit by eye to the upper envelope of the cluster distribution. The slanted solid line shows the slope for a fading relationship in which the minimum observable mass scales as log mass ∝ 0.69 log age. |
Hα and FUV emission are often used to trace star formation in galaxies, including dwarfs. However, commonly the Hα emission drops off faster than, and ends before, the FUV emission as one traces star formation into the outer disk (for example, Hunter et al (2010), and Fig. 2 here). In addition global ratios of Hα / FUV have been found to be a function of galactic surface brightness (for example, Meurer et al 2009, Treyer et al 2011). Lee et al (2009), for example, find that the Hα/FUV ratio is lower than expected by a factor of 2−10 in the nearby 11HUGS galaxies with the lowest SFRs (< 0.003 M⊙ yr−1).
The decline of the ratio Hα / FUV with radius in galaxies and variations between galaxies have been the subject of much debate. Causes that have been considered include variations in (Meurer et al 2009, Bruzzese et al 2015) or sampling issues with (Fumagalli et al 2011, da Silva et al 2014) the stellar initial mass function. Other explanations include variations in star formation history, loss of ionizing photons from the galaxy, and undetectability of diffuse Hα emission in outer disks (for example, Hunter et al 2010, Hunter et al 2011, Lee et al 2011, Eldridge 2012, Relaño et al 2012, Weisz et al 2012).
Since escape of ionizing photons from galaxies, and preferentially from small galaxies, is believed to have been responsible for the epoch of re-ionization in the early Universe, measuring the amount of leakage has been an important motivation for observations of Lyman continuum emission around galaxies in the nearby and more distant Universe. These observations give us the opportunity to see if leakage of ionizing photons from galaxies or outer disks could explain low Hα / FUV ratios. Lyman continuum escape fractions have been measured of order 6% − 13% in compact star-forming galaxies at z ∼ 0.3 and Lyα escape fractions of order 20% − 40% (Izotov et al 2016b). Rutkowski et al 2016 have placed a limit of ≤ 2.1% on the Lyman continuum escape fraction of a sample of most star-forming dwarf galaxies at z ∼ 1, and Izotov et al (2016a) measured an escape fraction of order 8% in a relatively low-mass star-forming galaxy at z ∼ 0.3. In a sample of four nearby galaxies, Leitet et al (2013) detected Lyman continuum in one, yielding an escape fraction of 2.4%, but Zastrow et al (2013) mapped [Siii] / [Sii] in six nearby dwarf starburst galaxies and found that the fraction of emission that escapes may depend on the orientation of the galaxy to the observer, the morphology of the ISM, and the age and concentration of the starburst producing the emission. Nevertheless, we see that escape fractions are not high enough to explain the lowest ratios of Hα / FUV. On the other hand, Hunter et al (2013), in a study of two luminous spirals, suggest that the drop in Hα emission with radius is due to low gas densities in outer disks and the resulting loss of Lyman continuum photons from the vicinity of star forming regions, making them undetectable in Hα, and not from a loss of photons out of the galaxy altogether.
Could we instead be under-estimating the amount of Hα emission that is actually there? To test the idea that significant amounts of Hα emission have been missed in outer disks, Lee et al (2016) performed very deep imaging in Hα of three nearby dwarf galaxies, reaching flux limits of order 10 times lower than that of the 11HUGS/LVL survey (Kennicutt et al 2008). Their new images (Fig. 7) do show emission extending up to 2.5 times further than the previous survey data, but this additional emission only contributes ∼ 5% more Hα flux. Therefore, the additional emission found in these deep images does not account for the radial trend in Hα/FUV.
 |
Figure 7. Hα images of UGC 5456 displayed on a linear scale to emphasize emission from diffuse ionized gas. Contours are at 10σ, 30σ, and 100σ above the background. On the left is the standard continuum subtracted narrow band image from the 11HUGS/LVL survey (Kennicutt et al 2008) and on the right is the deeper image from Lee et al (2016). Reproduced from Lee et al (2016) with permission from the AAS. |
The emission measure of individual Hii regions in outer disks can be very low, however, because of the extremely low average density. Following Hunter et al (2011), one can consider the possible values for emission measure if the far-outer disks in Fig. 2 are completely ionized. The limits of the stellar disks in these galaxies correspond to radii of 60 kpc in NGC 801 (R / RD = 4.2 in the figure) and 71 kpc in UGC 2885 (R / RD = 5.9). The total surface densities at these radii can be used to determine the gas disk thicknesses assuming a velocity dispersion of 10 km s−1. These thicknesses are T = 26.2 kpc and 11.4 kpc, respectively, if we consider thickness to be two isothermal scale heights. When combined with the Hi surface densities, the corresponding average densities are only n = 0.00052 cm−3 and 0.0031 cm−3. If the entire disk thicknesses were ionized at these densities, then the emission measures would be n2 T = 0.0069 cm−6 pc and 0.11 cm−6 pc. We convert emission measure to surface brightness as ΣHα(erg s−1 pc−2) = 7.7 × 1030 EM(cm−6 pc). Converting this to intensity units, we get IHα(erg s−1 cm−2 arcsec−2) = 1.5 × 10−18 EM(cm−6 pc). The limit of detection in the very deep survey by Lee et al (2016) was 8 × 10−18 erg s−1 cm−2 arcsec−2, which is still too high to see the fully ionized far-outer disks in Figure 2 by a factor of ∼ 50 or more.
8.4. Breaks in Radial Profiles in dIrr Galaxies
Figure 8 (right) illustrates another common feature of outer dIrr disks: abrupt breaks in azimuthally-averaged surface brightness profiles (Herrmann et al 2013). Most often the profile drops in brightness into the outer disk more steeply than in the inner disk (Type II profiles; Sect. 3) but occasionally it drops less steeply (Type III). Surface brightness profiles without breaks (Type I) are relatively rare. Radial profile breaks are common in spirals as well and were first discovered there (van der Kruit and Shostak 1982, Shostak and van der Kruit 1984, de Grijs et al 2001, Kregel et al 2002, Pohlen et al 2002, MacArthur et al 2003, Kregel and van der Kruit 2004, Erwin et al 2005, Pohlen and Trujillo 2006, Erwin et al 2008, Gutiérrez et al 2011). They are also found in high redshift disks (Pérez 2004). Bakos et al (2008) and Ruiz-Lara et al (2016) found that the Type II downturn at mid-radius decreases significantly in spirals when stellar mass profiles are considered instead of surface brightness. However, this is not the case for most dIrrs, as found by Herrmann et al (2016). Thus, RBr appears to represent a change in stellar population in spirals but a change in stellar surface mass density, at least in part, in dwarfs.
 |
Figure 8. Left: Representative V and FUV Type II and III surface brightness profiles with parameters for MB = −16 from Herrmann et al (2013). V highlights older stars, and FUV reveals younger stars. The steep FUV slope of the Type III profile interior to RBr implies an inner accretion trend. The steeper FUV slope in the Type II outskirts is evidence of outside-in shrinking of star formation activity. Right: Number of galaxies with the given fraction of the stellar mass beyond RBr. Type II profiles with bluing colour trends with radius (IIB) and with reddening colour trends with radius (IIR) are shown separately. Type IIR profiles have a larger fraction of their stellar mass beyond RBr than Type IIB or Type III. |
Herrmann et al (2013) examined the surface brightness profiles of 141 dwarfs in up to 11 passbands, and typical Type II and Type III profiles are sketched in Fig. 8 (left). Herrmann et al (2016) further examined the colour and mass surface density trends. They found that, although brighter galaxies tend to have larger RBr, the surface brightness in V, µV, at RBr is about 24 ± 1 mag arcsec−2, independent of MB and independent of galaxy type. The B − V colour at RBr is also nearly constant. However, when surface photometry is converted to stellar mass surface density for Type II profiles, values for dwarfs are a factor of ∼ 6 lower than those for spirals (Herrmann et al 2016, Bakos et al 2008). When separated by radially averaged colour trends, Type II profiles with reddening colour trends (IIR) have a larger fraction of their stellar mass beyond RBr than Type IIs with a bluing colour trend (IIB) or Type IIIs (Herrmann et al 2016; Fig. 8, right).
What is happening at RBr? Simulations of spirals by Roškar et al (2008), Martínez-Serrano et al (2009), Bakos et al (2011), and Minchev et al (2012) suggest that the break radius RBr grows with time and that for Type II profiles stars formed inside RBr migrate outward beyond RBr as a result of secular processes involving bar potentials or spiral arms (see observations by Radburn-Smith et al 2012). However, scattering of stars from spiral arms is not applicable to dIrrs and observations of some spirals are inconsistent with this scenario as well (Yoachim et al 2012). Another possibility is that there is a change in the dominate star formation process or efficiency at RBr (e.g., Schaye 2004, Piontek and Ostriker 2005, Elmegreen and Hunter 2006, Barnes et al 2012; but for models of star formation without a sharp change with radius see Ostriker et al 2010 and Krumholz 2013). Roškar et al (2008) suggest that, for spirals, it is a combination of a radial star formation cutoff and stellar mass redistribution (see also Zheng et al 2015). The different radial surface brightness and colour profiles in dwarfs can be understood empirically as the result of different evolutionary histories (Fig. 8, left): Type III galaxies are building their centres, perhaps through accretion of gas, while in Type IIR galaxies star formation is retreating to the inner regions of the galaxy (outside-in disk growth as suggested by Zhang et al (2012) and Type IIB galaxies may be systems in which star formation in the inner regions is winding down. Regardless, the near-constant surface brightness and colour at RBr in dwarfs and spirals argue that whatever is happening at RBr is common to both types of disk galaxies.