DOES STELLAR FEEDBACK CREATE H i HOLES? A HUBBLE SPACE TELESCOPE/VERY LARGE ARRAY STUDY OF HOLMBERG II

From our photometry we constructed CMDs of the stars in each of the 23 holes in the P92 catalog, 19 holes in the THINGS catalog, and nine control fields (Figures 3–6 and Tables 1, 2, and 5). Notably, we found that all holes in both catalogs contain a significant number of young stars; enough to easily identify CMD features by visual inspection and compare with the models of Marigo et al. (2008; see Figure 7). However, these CMDs are not consistent with the expected CMD for a single-age stellar cluster. The holes also have red giant branch (RGB) and asymptotic giant branch (AGB) stars with ages < 1 Gyr, as expected given that the older stars are fairly smoothly distributed throughout the optical galaxy (see Figure 11 in Weisz et al. 2008).

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Young stellar clusters (e.g., OB associations) are traditionally associated with the formation of H i holes (e.g., Brinks & Bajaja 1986; Hatzidimitriou et al. 2005), and we tested this notion by making a census of the youngest and brightest stars. We identified young stars based on the stellar evolution models of Marigo et al. (2008), which suggest that the brightest 10 Myr old MS star at its turnoff has M_F555W ∼ −5, or m_F555W ∼ 22.65 in Ho ii. We found 302 MS stars with m_F555W < 22.65 that also lay within holes in the P92 catalog. Further, restricting the color to be less than 0.05, i.e., m_F555W−m_F814W < 0.05, (to exclude Red Helium Burning stars (RHeBs), bright foreground stars, and most BHeBs) we find 109 stars that match our criteria. Of these 109 stars, 21 of them belong to hole 21, which is the largest and most populated hole with a diameter of ∼2 kpc and ∼40,000 stars in the CMD. Applying the above criteria for luminous MS stars to the remaining 21 holes, we found that all the holes have fewer than 10 bright MS stars and 20 holes have fewer than two bright MS stars. Similarly for the H i holes in the THINGS catalog, we found 347 stars with m_F555W < 22.65, and 104 stars with m_F555W < 22.65 and m_F555W−m_F814W < 0.05. Of these 104 stars, 30 belong to the largest hole (number 17). The other 18 holes all have fewer than 10 young MS stars, and 13 have fewer than two young MS stars. For the stars located in the control fields (Figure 6), we found that 32 match the bright MS star criteria, with c7 containing 21 of these stars, and six of the nine control fields containing two or less bright MS stars. The control field have more bright MS stars by a factor of ∼1.5 when compared to the H i holes. We explore the impact of small number statistics, stochastic effects on the SFR, and production of massive stars in Section 5.

From these basic calculations, it seems that the location of young OB type stars are not a reliable tracer of the locations of H i holes, nor do they accurately represent the presence of young remnant stellar populations inside H i holes. We will discuss the spatial distribution of these stars further in Section 5.2.

Upper MS stars and BHeBs offer the opportunity to age date stellar populations more than 10 Myr old. To extract a more complete picture of the recent SF within the H i holes, we measured the SFHs for the stars inside each H i hole and compared the timing of SF activity to the inferred kinematic ages, i.e., the radius of the hole divided by its expansion velocity. We derived the SFHs, from the CMDs, using SFH recovery code of Dolphin (2002). This method constructs synthetic CMDs, using the stellar evolution models of Marigo et al. (2008), and compares them to the observed CMD using a maximum likelihood technique. To obtain this solution, we used a combination of fixed (e.g., binary fraction, IMF) and searchable (e.g., distance, extinction) parameters. We allowed the program to search for the best fit metallicity per time bin, with the condition that the metallicity must monotonically increase with time toward the present. We found the mean metallicity in the most recent time bins from the SFHs to be consistent with the observed value of ∼10% Z_☉ (Miller & Hodge 1996), which is best fit by Z=0.002 isochrones (Figure 7). Throughout this paper, we use the following values when measuring SFHs or simulating CMDs: a standard power-law IMF with x = −2.3 from 0.1 to 100 M_☉, a binary fraction = 0.35, the stellar evolution models of Marigo et al. (2008), a distance of 3.40 Mpc, a foreground extinction of A_F555W = 0.11 (Schlegel et al. 1998), and 50% completeness limits of m_F555W = 27.9 and m_F814W = 27.4 (Weisz et al. 2008). To quantify the errors in the SFHs, we added the systematic uncertainties from the isochrones and the statistical uncertainties from Monte Carlo tests in quadrature. Quantifying the best fit solution and associated uncertainties from synthetic CMD matching has been subject to a number of extensive studies (e.g., Tosi et al. 1989; Tolstoy & Saha 1996; Gallart et al. 1996; Mighell 1997; Holtzman et al. 1999; Hernandez et al. 1999; Dolphin 2002; Ikuta & Arimoto 2002; Yuk & Lee 2007), which explore the nuances of this method beyond the scope of this paper. Full details of the method we used in this paper to measure the SFHs and quantify the associated errors can be found in Dolphin (2002).

As an example we present the observed, model, residual, and significance of the residual CMDs from the code of Dolphin (2002) for hole 23 in the THINGS catalog (Figure 8). Visual inspection of the observed and model CMD shows broad agreement of features such as the young MS, BHeBs, RHeBs, and the RGB. The difference between the model and the observed CMD can been seen in the lower two panels, where black points indicate more real stars than synthetic stars, and white points indicate more synthetic than real stars. The residual significance diagram (panel (d)), reveals no distinct patterns of black or white points, indicating that the model CMD describes the data quite well.

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We chose to focus on SF over the past 200 Myr in each of the holes (Figures 9–11) and control fields (Figure 12) based on the inferred kinematic ages of the holes derived from both hole catalogs. The time resolution of our SFHs is ∼10 Myr up to a look-back time of 50 Myr and then ∼25 Myr from 50 to 200 Myr. These choices provide an adequate look-back time and time resolution to see potential SF events responsible for the creation of the H i holes. Note that kinematic ages for H i holes are traditionally considered an upper limit to the age of the H i holes, as the expansion velocities were most likely higher in the past (e.g., Tenorio-Tagle & Bodenheimer 1988). We discuss the accuracy of inferred kinematic ages in more detail in Section 5.

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As a check for accuracy of SFHs between the two hole catalogs, we compared the SFHs and CMDs from overlapping holes. The CMD of P92 hole 44 significantly overlaps with THINGS holes 26 and 31. The CMD of P92 hole 44 has 7566 stars, where as the two THINGS holes have 4253 and 3190, respectively. In terms of the SFHs, the peak SFR for P92 hole 44 occurs in the 40–50 Myr bin with a peak value of 5.6×10⁻³ M_☉ yr⁻¹. Both the THINGS holes show peak SFRs in the same time bin, with values of 3.0×10⁻³ M_☉ yr⁻¹ and 3.2 ×10⁻³ M_☉ yr⁻¹, or co-adding them, we find a peak SFR of ∼6.2 ×10⁻³ M_☉ yr⁻¹, consistent with the values for the single P92 hole. Similar tests were carried out for several other overlapping holes, and all were found to have consistent SFRs where expected. It is important to note that because the stellar density is not uniform in Ho ii, even small differences in the location or radius of a hole may result in significant differences in the stellar populations and SFHs.

We searched for differences between the stellar populations of the control fields and the H i holes by comparing their cumulative SFHs (i.e., fraction of stars formed as a function of time) over the past 14.1 Gyr (lifetime) and 200 Myr (recent) by performing a Kolmogorov–Smirnov (K–S) test comparing the average cumulative SFHs for the holes and control fields (red lines in Figure 13). As expected, the majority of the holes and control fields share a common old stellar population, i.e., at least 50% of the stars were formed greater than 6 Gyr ago), and the fraction of stars formed in the last 6 Gyr is also consistent between the hole and control field samples. Although the past 200 Myr is likely more influential when it comes to hole formation, again we see no discernible difference between the recent cumulative SFHs of the two samples. The K–S test confirmed these impressions, indicating that, on both the lifetime and recent timescales, the stellar populations of the holes and control fields have the same parent distribution. From the perspective of the traditional stellar feedback hypothesis, this is an unanticipated result, as the theory would expect young stars associated with remnant clusters to be predominantly located inside the H i holes, and not control fields. This is discussed in more detail in Section 5.

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The minimum amount of energy required to evacuate an H i hole is given by the single blast model of Chevalier (1974):

$$\begin{equation} E_{\rm Hole} = 5.3\times 10^{43} n_{0}^{1.12} \left(\frac{d}{2}\right)^{3.12} v^{1.4}, \end{equation} \tag{ 1 }$$

where E_Hole is in the units of 10⁵⁰ erg, n₀ is the H i volume density (cm⁻³) at the mid-plane of the galaxy, d is the diameter of the H i hole in pc, and v is the expansion velocity in km s⁻¹. While the expansion velocity and diameter of the hole are independently measured quantities, n₀ is dependent upon the H i column density, $N_{\rm H\,\mathsc{i}}$, and scale height of the gas, h, in the following way:

$$\begin{equation} n_{0} = \frac{N_{\rm H\, \mathsc{i}}}{\sqrt{2\pi }h}. \end{equation} \tag{ 2 }$$

The denominator, $\sqrt{2\pi }h$ is the effective thickness of the gas assuming a Gaussian distribution, with h being the 1σ scale height.

One of the challenges in determining E_Hole is accurately measuring n₀. Both P92 and I. Bagetakos et al. (2009, in preparation) use a rotation curve to estimate the total mass in a gravitationally bound spherical system. This value was averaged over the volume of a sphere with a radius, $R_{V_{\rm max}}$ and multiplied by a factor of 2. Measuring σ_v = 6.8 km s⁻¹ (H i velocity dispersion), P92 found h = 625 pc, and I. Bagetakos et al. (2009, in preparation) find h = 600 pc. P92 used this method to compute the scale height of M31, and found it to be in agreement with the mass-model based method of Brinks & Burton (1984). However, P92 acknowledged that wide-field, deep photometry of Ho ii, would produce an accurate mass model of Ho ii, and a more precise knowledge of h, n₀, and E_Hole.

Fortunately, we had access to high-quality 3.6 μm imaging of Ho ii through the Local Volume Legacy Survey (LVL; Lee et al. 2008; Dale et al. 2009) taken with the Spitzer Space Telescope, which allowed us to construct such a mass model. The LVL team provided a calibrated (including foreground star subtraction) 3.6 μm image of Ho ii. From this image, we used the ISOPHOT package in IRAF⁹ to perform surface photometry, accounting for inclination and position angle effects (i = 47°, P.A. = 177°; Puche et al. 1992) starting at the dynamical center of the galaxy (α = 08:19:18, δ = +70:42:37; J2000), which yielded a surface brightness profile as a function of galactocentric radius (Figure 14). Following the method described in Section 4 of Oh et al. (2008) and assuming the 3.6 μm mass to light ratio, Γ_⋆ = 0.5 (comparable to other dwarf irregulars; Walter et al. 2008), we converted the surface brightness profile into a surface mass density profile, Σ.

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The isothermal gas scale height equation (Equation (3)) derived by Kellman (1970, and used by Kim et al. 1999 for the LMC) relates the surface mass density, Σ and the H i velocity dispersion, σ_v, to the H i scale height, h. For Ho ii, Bureau & Carignan (2002) derived σ_v as a function of galactocentric radius, allowing us to compute the H i scale height as a function of radius:

$$\begin{equation} h = \frac{\big\langle \sigma _{v}^{2} \big\rangle }{\pi G \Sigma }. \end{equation} \tag{ 3 }$$

We now have two independent estimates of the gas scale height, namely the H i scale height of P92 and that inferred from surface photometry. We found the H i scale height derived by P92 to be larger by a factor of ∼3–5 in the innermost 2 kpc of the galaxy, and in agreement at ∼4 kpc. At radii larger than 2 kpc, h is in better agreement between the different methods.

We computed new values of n₀, as a function of radius, using Equation (2) along with the newly calculated H i scale height and the values of $N_{\rm H\,\mathsc{i}}$ measured by P92. Because the P92 $N_{\rm H\,\mathsc{ i}}$ values showed multiple large fluctuations in the inner region of the galaxy, likely due to the presence a number of H i holes, we interpolated over the regions of large fluctuations to ensure a smooth, continuous distribution. Effectively, the largest difference in the P92 and new estimated values are due to the differences in the H i scales heights. The H i scale height derived from surface photometry effectively increases the values of n₀ by a factor of ∼3 compared to the P92 and I. Bagetakos et al. (2009, in preparation) values, which in turn increases E_Hole by approximately the same amount.

It is important to note that the values of E_Hole are likely lower limits on the energy necessary to evacuate an H i hole. The values of n₀ are the average H i volume density at a given radius. However, observationally, SF occurs at higher than average values of n₀, suggesting that to get a true sense of E_Hole we would need to measure a peak value of $N_{\rm H\,\mathsc{i}}$ inside the H i holes. Although this is not observationally plausible, we can get a sense of how a larger values of $N_{\rm H\,\mathsc{i}}$ would affect E_Hole. As an example, we examined control field 5, which is located near one of the highest regions of current SF in Ho ii. From Equation (3) and the peak $N_{\rm H\,\mathsc{i}}$ measured inside c5, we find an increase by a factor of ∼8 in the peak value of n₀ versus the average value. This translates into an increase in E_Hole by a factor of ∼10, suggesting that E_Hole values present here are likely lower limits.

A basic criteria of the stellar feedback model is that the energy associated with SF must exceed the energy necessary to evacuate a given H i hole. To calculate the available energy due to SF, we used the galaxy evolution modeling software STARBURST99 (Leitherer et al. 1999). We simulated a single instantaneous burst of SF with a fixed mass of 10⁶ M_☉ using STARBURST99 parameters that matched those described in Section 3.2, including a metallicity of Z=0.002, a SN cutoff mass of 8 M_☉, and a time sampling of 5 Myr.

Because the energy output from STARBURST99 scales linearly with the input mass, we ran one simulation (with a stellar mass of 10⁶ M_☉), and then subsequently scaled it by the integrated stellar mass from the SFHs of stars inside each hole, sampled at 5 Myr intervals. The cumulative distribution of the energy generated from SF from the present (t = 0) to 200 Myr for the stars inside each H i hole is shown in Figures 15–20. The inferred kinematic ages are denoted by the gray dashed line, and efficiencies (see Section 4.3) of 100%, 10%, and 1% are indicated by the red, green, and blue dashed lines, respectively.

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We have examined the efficiency over the inferred kinematic age for both catalogs as a function of galactocentric radius, hole radius, expansion velocity, and inferred kinematic age (Figure 21). For both hole catalogs the clearest trend we found is that efficiency seems to increase with expansion velocity. However, this result is likely misleading, because of the differences in assigning expansion velocities. In the THINGS, catalog, if a hole was blown out, it was assigned an expansion velocity of 7 km s⁻¹, whereas P92 attempted to measure the best fit expansion velocity for each hole. Thus, if we assigned each P92 hole with an expansion velocity lower than 7 km s⁻¹, the value of 7 km s⁻¹, there would be no trend in the P92 sample, consistent with the THINGS sample. Based on the THINGS catalog classification (see Section 2) of hole types, we found that holes that have not blown out (type 2 or 3), tend to have efficiencies higher than expected from models (see Section 4.3 for a description of the models), in some cases exceeding 100%. In contrast, holes that have blown out generally fall within the expected range. Again, this trend is likely due to the measurement techniques of the H i expansion velocities. In general, a blown out hole has stalled expansion, and its expansion velocity is not detectable above the random H i motions. Thus, the measurements of E_Hole are highly uncertain for blown out holes as are the efficiencies. The underlying implication is that the creation of an H i hole is a complex event that cannot be accurately represented by a simple kinematic age or efficiency, rather a more complex model is necessary (see Section 5 for more discussion).

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We then compared the inferred energy from SF over the kinematic age of each hole, E_SFKA, to the energy needed to produce the observed properties of each hole, E_Hole. The ratio of E_Hole to E_SFKA allows us to calculate the "putative" stellar feedback efficiency, , over the inferred kinematic age of each hole (see Tables 3 and 4). Models of SF including feedback and interactions with the ISM expect such efficiencies to range from ∼1% to 20% (Theis et al. 1992; Cole et al. 1994; Padoan et al. 1997; Thornton et al. 1998). Fifteen of the 23 P92 holes and 6 of the 19 THINGS holes have putative efficiencies between 1% and 20%, in agreement with the models. Overall, a higher fraction of P92 holes are within the expected efficiency range than THINGS holes. While this may seem to be an unexpected result, this actually underlines the complexity of the connection between stars and H i holes. For example, P92 hole 42 and THINGS hole 27 are roughly the same size, but slightly different central coordinates, which results in the THINGS hole having more stars in its CMD by a factor of ∼2, in turn influencing the SFH and feedback efficiency. Of the holes that are not consistent with the expected range, one P92 hole (number 48) has an efficiency greater than 100%, while five THINGS holes (9, 12, 14, 23, 39) also have efficiencies greater than 100% (Figure 21). These outliers suggest that perhaps energy from stellar feedback is not sufficient to have created these holes.

For example, P92 hole 14 (Figure 15) has an efficiency of ∼1% where the inferred kinematic age intersects the cumulative energy profile. In comparison, P92 hole 30 (Figure 16) has a kinematic age efficiency of 39%, outside the theoretical range predicted by models. Further, ratios that require > 100% indicate that there has not been enough energy for SF during the inferred kinematic age of each hole. However, Figures 15–20 show that there has been sufficient energy available during the most recent 200 Myr even in these extreme cases, suggesting that perhaps the inferred kinematic ages do not truly represent the ages of the holes, or that the concept of an H i hole age is intrinsically ambiguous for holes that contain multiple generations of stars.

To explore this possibility, instead of using the inferred kinematic age as a guide, we assumed a nominal 10% efficiency and recalculated the age of the hole to match the timescale needed to give sufficient energy input from SF. For example, while P92 hole 48 (Figure 17) has a kinematic age efficiency of 120%, the energy profile shows that over the past 200 Myr, enough energy was generated from SF to have created the hole, if the hole is ∼100 Myr old (assuming a nominal 10% efficiency). Similarly, for the other P92 and THINGS holes that have efficiencies outside the theoretical range, the same analysis shows that there is ample energy from SF to have created each of those holes in the past 200 Myr. We defined a "look-back age" as the time at which the line of 10% efficiency intersects the energy profiles in Figures 15–20. We then compared the ratio of the look-back age to the inferred kinematic age, and found that the inferred kinematic ages are generally lower than the look-back times (Figure 22). While perhaps not the most rigorous definition of the age of a hole, the look-back age suggests that the inferred kinematic age may not accurately represent the true age of H i holes, even as an upper limit. We explore the kinematic age discrepancy in greater detail in Section 5.

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In addition to the measuring the SFR as a function of time, we can use spatial information from the resolved stellar populations to qualitatively compare the location of SF episodes with H i column densities. Following a method of analysis similar to Dohm-Palmer et al. (1997), we used BHeBs from the entire HST/ACS CMD of Ho ii (Weisz et al. 2008) and constructed movies of the spatially resolved recent SFH over the past ∼200 Myr. The initial masses of BHeBs range from ∼2 to 20 M_☉, giving them lifetimes between ∼5 and 500 Myr. More importantly, BHeBs have a one-to-one correspondence between luminosity and age. BHeBs of a single age therefore occupy a unique location on a CMD, making them superb tracers of recent SF. In contrast, multiple generations of MS stars can occupy the same location on the CMD, making age dating of most individual MS stars from the CMD virtually impossible (see Dohm-Palmer et al. 1997; Gallart et al. 2005; Weisz et al. 2008, for a more in depth discussion of age dating stars from CMDs).

By measuring its magnitude, we can assign a unique age to each BHeB, using the models of stellar evolution. We can then trace the location of SF as a function of age based on BHeB positions in the ACS image. While it is true that many young star clusters dissolve into the field on timescales of ∼10 Myr (e.g., Lada & Lada 2003), the stars can maintain spatial coherence for much longer. Empirically, CMD-based studies of the SMC and LMC find that star-forming structures (such as associations) can remain coherent for up to a couple hundred Myr (Gieles et al. 2008; Bastian et al. 2009).

We were able to isolate the BHeBs on the CMD by visual inspection because Ho ii has a large number of BHeBs, and low foreground and internal reddening values. We constructed a smooth analytic function mapping the magnitudes of the BHeB track to unique ages, using the stellar evolution models of Marigo et al. (2008). Applying this function to the observed BHeBs, we assigned each star an individual age, with an uncertainty of ≲ 20%. We created density maps of the BHeBs by placing the stars into 5 Myr bins and converting their x and y coordinates to right ascension (R.A.) and declination (decl). We then smoothed the resulting images with a Gaussian kernel with a FWHM ∼15''.

To convert the BHeB density maps (stars pixel⁻¹) to SFR/area (M_☉ yr⁻¹ kpc⁻²), we first divided each frame (i.e., 5 Myr binned density maps) by the sum of the pixel values to determine the fractional contribution of each pixel to the total stellar density in each frame. That is, if a normalized pixel had a value of 0 it did not contribute to the SF in the frame, while a pixel with a value of 0.01 contributed to 1% of the SF in that frame. The density maps were then connected to the SFH of the field (Weisz et al. 2008).

First, we re-binned the SFH with different time resolutions: 10 Myr for a look-back time of ∼100 Myr and 20 Myr for a look-back time of ∼200 Myr, in order to match the decreasing time resolution at older ages. We then interpolated each to a 5 Myr time sampling to match the temporal resolution of the stellar density maps. We then multiplied each stellar density map by the corresponding SFR and divided by the physical area of the ACS field of view, thus converting the images from units of stars pixel⁻¹ to SFR/area. We then performed bilinear interpolation over time and space to ensure smooth and continuous movies. The result is two movies of the spatially resolved SFHs of Ho ii with units of SFR/area, with look-back times of ∼100 and ∼200 Myr, and a spatial resolution of ∼15'' (∼250 pc). Figures 23 and 24 show select still frames of the two movies with H i contours overlaid.

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The general trends presented by the spatially resolved SFHs are that low level SF has dominated the galaxy in the most recent ∼200 Myr, with only a substantial rise in the SF activity in the last ∼40 Myr. The smoothness of the SFH implies that the H i holes were not produced by a series of intense episodes of SF, instead the holes were created due to low level SF with some variation above a constant value, which has steadily input energy into the ISM. As a comparison, we integrated the spatial resolved SFH of the region corresponding to THINGS hole 17 and found general agreement between the two. For example, both SFHs show a peak at ∼40 Myr, and from the integration of the spatially resolved SFH we found the SFR at this time to be 3.0×10⁻² M_☉ yr⁻¹, whereas the SFH from Figure 5 shows a SFR of 4.0×10⁻² M_☉ yr⁻¹. While this difference of 30% may seem large, in fact, the systematic and statistical uncertainties from the two methods are ∼20% from the temporal SFH and 50% from the spatial SFH, which implies these are consistent values.

These movies allow us to investigate the correlation between H i density and SF on different timescales. Within the last ∼40 Myr, the SF is well correlated with high H i surface density, as has been seen in Hα, and UV imaging (see Section 5.2 for a discussion on Hα and UV imaging). On longer timescales, we note that the SF patterns do not adhere to the locations of high H i column densities. In particular, there is a relatively high level of SF activity in the large H i void, corresponding to P92 hole 21 and THINGS hole 17, ∼40 Myr ago, which has been preceded by low level activity for at least the past ∼200 Myr.

The study of Ho ii by Rhode et al. (1999) is perhaps one of the most rigorous observational tests of the stellar feedback model of H i hole creation. Despite the appeal of the stellar feedback theory of H i hole formation, Rhode et al. (1999) found no compelling evidence supporting this hypothesis, and their conclusions seriously challenged the standard model of H i hole formation. The non-detection of stars in the majority of H i holes contradicted expectations for stellar feedback as a universal mechanism of hole creation, although Rhode et al. (1999) did not rule out stellar feedback as the source of small H i holes in the central regions of Ho ii.

Rhode et al. (1999) searched for single-age stellar clusters, but likely did not find them because the single-age cluster model can overestimate the surface brightness of the remnant stars by a significant amount, for a variety of reasons we explore in the following sections. Further, using only integrated light, it can be difficult to distinguish between a single-age stellar cluster and a mixed age stellar population, which can make it difficult to age date stars that are detected. As a comparative test, we computed the integrated magnitudes of each of the Rhode et al. (1999) apertures from the HST/ACS CMDs. Our integrated photometry is in agreement with that of Rhode et al. (1999). A histogram of the resulting integrated magnitudes reveals that the six regions where Rhode et al. (1999) did detect stars are among the brightest in the sample (Figure 25). The rest of the regions were classified as non-detections, despite containing a significant number of young stars.

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Using the HST/ACS photometry of Ho ii we constructed CMDs of the apertures (panel (d) of Figure 1 and Table 6) defined by Rhode et al. (1999). Figures 26 and 27 unequivocally show well-populated CMDs of mixed age stellar populations, including young MS stars and HeBs, which are likely the remnant stars Rhode et al. (1999) attempted to detect using integrated light. Our interpretation is that single-age stellar populations do not produce a majority of the H i holes in Ho ii, confirming the conclusions of Rhode et al. (1999).

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Instead of assuming that a single-age cluster was responsible for the creation of H i holes, we explored the possibility that a mixed age stellar population producing SNe tens or hundreds of Myr apart was responsible for the creation of H i holes. Specifically, we asked how a remnant mixed age stellar population would differ from a single-age cluster in terms of the integrated light properties, location of stars inside H i holes, and energetics associated with this different mode of SF.

To illustrate this, we generated synthetic CMDs, with the same parameters (e.g., IMF, binary fraction, distance, etc.) used to measure the SFHs in Section 2, and computed the mean expected integrated magnitudes of different stellar populations. To ensure that we were not in a regime where stochastic effects are important, we fixed the integrated mass of the simulations to be 10⁶ M_☉, ∼1% of the stellar mass of Ho ii and at least a factor of 100 greater than the stellar mass within any given hole. We limited the simulations to the most recent 100 Myr, the approximate age regime of the majority of H i holes in Ho ii. The simulations were run 100 times, which produced an average statistical error of ∼0.01 mag. Effects of completeness and photometric error are similarly ∼0.01 mag. Neither source of error has a large impact on the results at magnitudes this bright.

The first model assumed that all the stellar mass was formed in a ∼5 Myr period 50 Myr ago, with no subsequent SF. For this, "burst" model, we found the mean integrated magnitude and color to be m_F555W = 15.88 and m_F555W − m_F814W = 0.48. For comparison, we distributed the same integrated stellar mass with a constant SFR over the period of 50–100 Myr and found m_F555W = 16.07 and m_F555W − m_F814W = 0.51.

We further considered a two-component SFH model. We distributed 10⁶ M_☉ in stellar mass with a constant SFR from 50 to 90 Myr ago, no SF from 35 to 50 Myr ago, constant SFR from 25 to 35 Myr ago, and quiescence for the most recent 25 Myr. This multiple episode model produced stars with integrated properties of m_F555W = 15.86 and m_F555W − m_F814W = 0.54. Comparing the single age, constant, and multiple episode models of the same integrated stellar mass, we found they produced results that were indistinguishable in terms of integrated light.

To illustrate this point empirically, we compared the stellar populations of P92 holes 42 and 43, which both have integrated magnitudes of m_F555W = 18.75, but differ in other properties. For example, hole 42 contains 1383 stars and has an inferred kinematic age of 17 Myr, but hole 43 has 549 stars and an inferred kinematic age of 26 Myr. The SFHs of stars within the two holes differ significantly in the last 10 Myr. SF in hole 42 had been more prominent > 10 Myr ago, however within the last 10 Myr, hole 43 has a higher SFR, likely producing young bright stars that dominate the integrated light of the stellar population. These findings suggest that integrated light can only serve as an indicator of recent SF, but cannot give an accurate account of the SFH.

The dissolution of stellar clusters into the field further complicates integrated light observations and analysis of clusters. Lada & Lada (2003) note that the most common stellar clusters contain only dozens of stars and disperse into the field within ∼10 Myr, which is the so-called "infant mortality" scenario of cluster dissolution. Detailed studies of structure of stellar groups in the SMC and LMC show that only ∼3%–7% of young stars survive in clusters past the age of ∼10 Myr (Gieles et al. 2008; Bastian et al. 2009). Applying this idea to Ho ii, it suggests that the remnant stellar populations would not be highly clustered, but instead would be distributed across the H i hole, resulting in fainter integrated magnitudes than expected for clustered stars. To look for this effect we selected MS stars from the HST/ACS photometry by applying magnitude and color restrictions that isolated young MS stars (< 10 Myr (red) and < 75 Myr (blue)) and plotted their positions relative to the H i holes catalogs, Rhode et al. (1999) apertures, and control fields (Figure 28). While there is some clustering of young stars, particularly those < 10 Myr in age, the clusters of stars are typically on the edges of the H i holes where triggered secondary SF due to the expansion of the hole is likely taking place (e.g., Tenorio-Tagle & Bodenheimer 1988). The majority of the MS stars < 75 Myr in age are not clustered, which makes the integrated light of these stellar populations appear fainter than had they been bound or appeared as unresolved stellar clusters.

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One of the most interesting cases presented by Rhode et al. (1999) is that of P92 hole 10. Based on its H i properties at least several dozen SNe would be necessary to have created hole 10. The remnant stars from a burst should be well above the detection criteria used by Rhode et al. (1999) in a single cluster model, but none were detected. Rhode et al. (1999) assumed a single remnant cluster would be in the center of the hole and used an aperture smaller than the hole to search for the stars. Comparing the CMD between the actual hole and the aperture shows why the stars likely responsible for creating hole 10 were not detected by Rhode et al. (1999). The CMD of the entire hole has ∼4200 stars and an integrated magnitude of m_F555W = 17.68, while the CMD of the Rhode et al. (1999) hole 10 aperture contains 893 stars and has an integrated magnitude of m_F555W = 19.75. Furthermore, the spatial distribution of MS stars < 75 Myr in age (Figure 28) show that the photometric aperture of hole 10 has no stars, while the hole itself contains a number of young stars. It appears that the bright stars either did not form centrally in hole 10 or they have rapidly diffused out of the center, if they did form there. Although this hole was considered among the strongest evidence against the stellar feedback theory of H i hole creation, it now only seems to confirm that the single-age cluster model of hole formation is not the appropriate mechanism for H i hole creation.

If H i holes form via multiple generations of SNe, understanding the underlying physics becomes more complicated. We have to go beyond the simple single blast model of H i hole creation and consider the complex interplay between the local ISM and stellar feedback, which seems to be the dominant mechanism behind structure formation in the ISM (e.g., Harris & Zaritsky 2008). Heiles (1990) considers the case of "clusters of clusters" of SNe present within an H i hole, noting that sequential explosions would contribute to the mechanical energy expanding the hole as well as significantly alter the gas density inside the hole. Oey & Clarke (1997) also conclude that multiple OB associations would increase the mechanical power and timescale of energy input into expanding the shell. Recchi & Hensler (2006) present a model demonstrating how two separate SF events inside an H i hole would delay the onset of the hole refilling with cold gas with timescales from ∼100 to 600 Myr depending on local conditions, indicating the multiple episodes of SF spread out over time can help extend the life of an H i hole. Projection effects could cause generations of stars along a line of site appear to be spatially coincident within a given H i hole. However, this is likely a small effect because the disk-like nature of Ho ii implies that the stellar scale height is much less than that of the H i, suggesting a reasonable assumption is that the young stars are primarily located in the mid-plane of the disk.

Quantitative modeling of the impact of the complex scenarios presented by multiple generations of SF inside H i holes has yet to be carried out in detail. Presently, the single blast approximation and kinematic age estimations of H i holes are dependent upon quantities (e.g., expansion velocity, volume density) that likely have varied over the history of a given hole. Quantifying the precise impact of these parameters on H i hole formation and energetics is beyond the scope of this paper. For example, while why control fields and H i holes contain similar stellar populations, but vastly different H i column densities, is an open question. However, Ho ii may not be the best galaxy to answer this question, because we are not sensitive to H i hole smaller than ∼100 pc. Thus, if it is the case that larger holes are mergers of multiple smaller holes, we simply may not be sensitive to the small holes forming inside the control fields. Analysis similar to that presented in this paper using galaxies with smaller resolvable H i holes (e.g., LMC or SMC) along with computer modeling that accounts for the effects of an anisotropic ISM and multiple generations of SNe could lend insight into the fundamental physical processes that are responsible for shaping the ISM and driving H i hole formation.

Of particular interest to Rhode et al. (1999) are the presence of H i holes outside the optical body of the galaxy. While they do not rule out the possibility that the inner holes could have formed from SF, the typical H i densities in the outer regions of Ho ii are relatively low, which is not very conducive to SF (Kennicutt 1989). However, the properties of holes in outer regions of galaxies do not differ from those in inner regions (Brinks & Bajaja 1986; Puche et al. 1992; Hatzidimitriou et al. 2005; I. Bagetakos et al. 2009, in preparation), suggesting that the same underlying mechanism, namely stellar feedback, is responsible for H i holes in both environments. To this end, we used a Monte Carlo method to compute the expected stellar populations in the outer holes of Ho ii to see if their creation via stellar feedback is possible.

From E_Hole we can calculate the SFR over the kinematic age, SFR_KA, for a typical outer H i hole and then use it to construct simulated CMDs to determine properties of the expected stellar populations. We find that the 19 holes from I. Bagetakos et al. (2009, in preparation) located outside our ACS coverage have a mean diameter of ∼800 pc, an expansion velocity ∼8 km s⁻¹, a kinematic age ∼50 Myr, an H i volume density of 0.1 cm⁻³, and E_Hole ∼ 100 ×10⁵⁰ erg. Assuming 10⁵¹ erg per SN (McCray & Kafatos 1987) and that 10% of this energy goes into moving the ISM (Theis et al. 1992; Cole et al. 1994; Padoan et al. 1997; Thornton et al. 1998), ∼100 SN are needed to create an H i hole with these properties, equivalent to a SN rate over the kinematic age of ∼10⁻⁶ SN yr⁻¹. Assuming that the SNe come from stars with M > 8 M_☉, we find SFR_KA ∼ 2×10⁻⁵ M_☉ yr⁻¹ for all stars, using our standard IMF (Section 3.2). This SFR implies an integrated stellar mass of ∼10³ M_☉ over the kinematic age.

With this SFR as input, we constructed simulated CMDs, via a Monte Carlo process using either a constant or a burst model. The input for the constant SFR model had a SFR = 2×10⁻⁵ M_☉ yr⁻¹ from 50 Myr to 100 Myr. This focuses on the brightest stars and most recent SF likely to have created the H i hole. The burst model assumed a burst of SF 50 Myr ago, producing 1000 M_☉. We ran each simulation 100 times to account for the statistical fluctuations. For the constant model, we find that the average CMD of the remnant stars has ∼7 stars and an integrated magnitude of m_F555W = 24.00, assuming a limiting photometric depth equal to the 50% completeness limit (Weisz et al. 2008). For the burst model, the average CMD of the remnant stars had ∼8 stars and a integrated magnitude of m_F555W = 23.75. Both cases result in integrated magnitudes fainter than the predictions by Rhode et al. (1999) as well as the hole and control fields presented in this paper. The remnant stellar populations in the outer holes are likely only detectable with deep photometry of resolved stars.

Other common methods of searching for stellar populations inside H i holes include the use of Hα, 24 μm, and UV imaging (e.g., Puche et al. 1992; Stewart et al. 2000; Muller et al. 2003). UV traces a stellar population with initial masses ≳3 M_☉ and timescales of ∼100 Myr, while Hα (and 24 μm in more dusty environments) traces ionizing photons from MS stars with initial masses of ≳ 20 M_☉ and ages ≲ 10 Myr (see Kennicutt 1998, for a full review of different SFR indicators and their properties). A number of studies aimed at testing the stellar feedback theory of hole creation via this type of imaging have done so with a mixed degree of success (Puche et al. 1992; Kim et al. 1999; Rhode et al. 1999; Stewart et al. 2000; Muller et al. 2003; Cannon et al. 2005; Book et al. 2008). Given the low SFRs we have derived (10⁻⁴ to 10⁻⁵ M_☉ yr⁻¹) within many of the H i holes, it is not entirely surprising that these imaging techniques have yielded such mixed results. Simulations have shown that for SFRs below ∼10⁻⁴ M_☉ yr⁻¹ stochastic processes become important and Hα is no longer a reliable tracer of SF (Tremonti et al. 2007; Thilker et al. 2007; Meurer et al. 2009). Although a similar study in the UV has yet to be conducted, given the small number of stars expected in any given CMD, it is likely that the UV has a similar cutoff SFR. Indeed, Stewart et al. (2000) used FUV imaging of Ho ii to show that there is some agreement between H i hole locations and bright UV regions, but did not find a good one-to-one correlation.

We can test for UV-bright stellar populations within the outer holes using data from the Local Volume Legacy sample (Lee et al. 2008; Dale et al. 2009), which contains FUV and NUV imaging originating from the GALEX Nearby Galaxies Survey (Gil de Paz et al. 2007), and the Hα and 24 μm images from the Spitzer Infrared Nearby Galaxies Survey (SINGS; Kennicutt et al. 2003). Overlaying the H i hole and Rhode et al. (1999) aperture locations over these images, we compared the location of bright regions with known H i holes (Figures 29–31). Because the correlation between low SFRs and Hα, 24 μm, and UV is not well understood, we are only able to make qualitative conclusions. From all the images, it is evident that there is not a one-to-one correlation between any of these fluxes and the stellar populations inside the H i holes as shown in the HST/ACS based CMDs. This simple test demonstrates that deep photometry is necessary to understand the formation and histories of H i holes.

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Perhaps the biggest challenge to the stellar feedback model of H i hole creation comes from observations of some of the closest galaxies. The proximity of the SMC and LMC allow for detailed observations, including high-resolution H i imaging, which probes physical scales as small as ∼15 pc (Kim et al. 1999). Matching catalogs of young stellar objects (e.g., OB associations, supergiants, WR stars) and Hα imaging to H i hole catalogs, three recent studies of the LMC (Kim et al. 1999), the SMC (Hatzidimitriou et al. 2005), and the Magellanic Bridge (Muller et al. 2003) do not find strong correlations between the locations of young stellar objects and H i holes. The largest challenge to the stellar feedback creation hypothesis posed by these studies are the presence of young H i holes (∼2–10 Myr) with no associated young stellar objects (Stanimirović 2007). This is particularly problematic in the SMC, where Hatzidimitriou et al. (2005) identified 59 young holes (∼5–10 Myr) that appear to be void of young stellar objects. Hatzidimitriou et al. (2005) further find that the physical characteristics of these particular holes are no different than those with stellar components. Further, Hatzidimitriou et al. (2005) conclude that the properties of the H i holes in the inner and outer region are indistinguishable and that from their analysis there is no evidence to suspect a different creation mechanism for inner and outer holes.

Using the same type of analysis as in Section 5.3, and the assumption that inner and outer holes are indistinguishable in their H i properties Hatzidimitriou et al. (2005), we can compute the properties of the expected stellar populations if these young holes were formed due to stellar feedback. For the 59 empty H i holes in the SMC, we find that the mean size is ∼128 pc, the expansion velocity is 7.5 km s⁻¹, and the inferred kinematic age is 8 Myr. We also compute E_Hole ∼ 56 ×10⁵⁰, assuming an H i volume density of 1.0 cm⁻³, and find that SFR_KA = 7×10⁻⁵ M_☉ yr⁻¹. We simulate 100 CMDs assuming a distance modulus of 19, photometric completeness limits of m_V = 22 and m_I = 21.7 (Harris & Zaritsky 2004), and the parameters listed in Section 3.2. We chose to only consider a burst model of SF at 8 Myr, since the differences between a burst and constant model of SF over such a short timescale are minimal. We ran 100 simulations, to account for small number statistics, and found that the typical CMD contained ∼40 stars (within the completeness limits) and the mean magnitude of the brightest star in the CMD was m_F555W ∼14.80. We found that only 25 out of the 100 simulated CMDs contained at least one star with m_F555W < 14, i.e., a bright OB type star. For m_F555W < 15, we found 72 CMDs contained at least one such star. This test signifies that for a episode of SF 8 Myr ago, only 25% of the time we would expect to find a star brighter than m_F555W = 14, and 72% of the time for m_F555W = 15.

Applying these statistics to the 509 holes cataloged by Hatzidimitriou et al. (2005), we expect 128 H i holes with at least one star brighter than m_F555W = 14, or 367 holes for m_F555W = 15. In comparison, Hatzidimitriou et al. (2005) find 330 H i holes with at least one star cluster, young star, or WR star. Initially, they also found 80 holes that appeared void of stars, however follow-up observations revealed that 21 of the 80 holes appeared to have A spectral-type stars, leaving 59 holes without detected stellar companions, which is consistent with the 143 of holes we predict will appear void of MS stars at m_F555W = 15. The uncertainties in our calculation are at least 50%, due to uncertainties in E_Hole, the stellar evolution models, and statistical error. Further, we are not able to test out results directly as we cannot reasonably compare our predicted stellar populations to the various catalogs used for correlations by Hatzidimitriou et al. (2005). However, we have demonstrated that even without the detection of a bright object inside a young H i hole, it is possible that the hole was created by stellar feedback.