DUST-TO-GAS RATIO IN THE EXTREMELY METAL-POOR GALAXY I Zw 18

We use a variety of data from several different facilities to map the far-infrared, sub millimeter, millimeter, and radio wave emission of I Zw 18. Therefore, our data set uses the following observatories and instruments: Spitzer Multiband Imaging Spectrometer (MIPS; Rieke et al. 2004), Herschel Photodetector Array Camera and Spectrometer (PACS; Poglitsch et al. 2010), Herschel Spectral and Photometric Imaging Receiver (SPIRE; Griffin et al. 2010), IRAM Plateau de Bure Interferometer (PdBI), and Very Large Array (VLA). In this section we will briefly describe new observations.

Spitzer: We observed I Zw 18 at 70 and 160 μm using MIPS in photometry mode as part of a cycle 5 proposal (PI: A. Bolatto; AOR: 22369536). The total observation time was 8 hours. The reduction of these images very closely follows the procedure described in Gordon et al. (2007) and Stansberry et al. (2007) for the 70 and 160 μm map, respectively.

Herschel/PACS: We use archival 70 and 160 μm observations from Herschel. The observations were taken with PACS using the Large Scan Map mode as part of the Herschel Guaranteed Time Key Program, Dwarf Galaxy Survey (PI: S. Madden; ObsID: 1342187135/36). The scan maps were taken at 90° angles from one another at the medium scan speed (20'' s⁻¹) and then combined together in order to reduce the noise caused by streaking along the scan direction. The scan leg length is 4.0', and the total on-source time for the combined images was 192 s.

Unlike Spitzer data, the methods to reduce PACS data are still evolving significantly. Therefore, we reduce the data in two separate ways. We first use Herschel Interactive Processing Environment (HIPE) v4.2 with the standard pipeline scripts. We also process the data up to level 1 in HIPE v7. We use the standard pipeline, which includes pixel flagging, flux density conversion, and sky coordinate association for each pixel of the detector. At this stage, the PACS timelines are still affected by 1/f noise and baseline drifts. In order to subtract the baseline, remove glitches, and project the timelines on the final map, we applied the scanamorphos algorithm (H. Roussel 2012, in preparation) to the level-1 PACS timelines.

Herschel/SPIRE: We use archival Herschel Spectral and Photometric Imaging Receiver (SPIRE; Griffin et al. 2010) photometric observations at 250, 350, and 500 μm. Observations were made in the large map mode with the nominal scan speed of 30 arcsec s⁻¹ and the cross-scanning method as part of Herschel Science Demonstration Phase (PI: S. Madden; ObsID: 1342188663). Data reprocessing was carried out in HIPE using the standard large map pipeline with the latest SPIRE calibration tree available,¹⁰ which includes deglitching the timeline data, flux calibration, and various corrections. After removal of a linear baseline, images were made using the standard naive mapper. The final maps are in units of Jy beam⁻¹ with pixel scales of 6, 10, and 14 arcsec at 250, 350, and 500 μm, respectively, as described in the SPIRE Data Reduction Guide.

PdBI: We present new observations of the CO J = 1 → 0 transition in I Zw 18 using the IRAM Plateau de Bure Interferometer as project t027 (PI: A. Leroy). The data were observed on 2009 September 24, 27, and 28 using the "5Dq" configuration, meaning that five telescopes were operational and that the array was in a compact configuration. These data are calibrated in the standard way in 2009 December using the PdBI pipeline implemented in the CLIC and MAPPING packages of GILDAS. The effective time on-source was 12.5 hr after flagging during the pipeline run. The effective bandwidth was ∼850 MHz, or about 2200 km s⁻¹ with native resolution ∼2.5 MHz (6.5 km s⁻¹). We do not detect CO emission. At 26 km s⁻¹ velocity resolution we achieved an rms noise of 1.26 mJy beam⁻¹, implying a 4σ flux upper limit for a point source of 0.131 Jy km s⁻¹.

VLA: The observations used to construct the H i map are described in van Zee et al. (1998). We obtained two hours of Rapid Response 21 cm VLA observations (project 08B-246; PI: A. Bolatto) to evaluate the Galactic foreground contribution. This contribution can be estimated by measuring the H i column density toward I Zw 18 and converting it to dust emission using typical high-latitude Galactic ratios (e.g., Boulanger et al. 1996). The observations were obtained during the move between CnD and D configuration with a synthesized beam size of 67'' × 41'' and a native resolution of 6.1 kHz (1.3 km s⁻¹). The data were reduced in AIPS using the standard procedure and calibrations, and care was taken to remove the baselines affected by the frequency aliasing problems due to the VLA–JVLA transition. At 10.3 km s⁻¹ velocity resolution we achieved an rms noise of 1.1 mJy beam⁻¹, implying an H i column density of N_H i = 2.4 × 10¹⁸ cm⁻². Galactic neutral hydrogen emission was observed in the central 30 km s⁻¹ of the passband. Nonetheless, even after spatially filtering the 160 μm MIPS map to approximately match the uv coverage of the VLA, the correlation between the high-resolution H i column density and the 160 μm surface brightness remained extremely low (Figure 2), showing that most of the emission present in the 160 and 250 μm images is not due to the high-latitude Galactic foreground.

In Figure 1 we present the Spitzer MIPS 70 and 160 μm maps and the Herschel PACS 160 μm image for I Zw 18. Overlaid on each image is the H i column density distribution observed by van Zee et al. (1998). The H i contours correspond to 0.7, 1.4, and 5 × 10²⁰ cm⁻² enclosing 98%, 96%, and 78% of the total flux at 70 μm. We use the MIPS 70 μm map over the PACS 70 μm because it has a much better surface brightness sensitivity (0.17 versus 2.87 MJy sr⁻¹), yielding a better signal-to-noise ratio. The bulk of the 70 μm emission coincides with the H i column density maximum. This peak also coincides with the location of active star-forming regions observed by Cannon et al. (2002) using the Hubble Space Telescope (HST). The diffuse component at 70 μm extends preferentially ∼3 kpc northwest from the peak. We subtract the background emission measured in a region free of sources. We integrate the flux using a circular aperture with radius of 45'' centered at the peak of the 70 μm emission and applying an aperture correction factor of 1.13 (determined by integrating over the point-spread function and compatible with those in the MIPS Instrument Handbook). The calibration error on Spitzer is about 5% at 70μm. We estimate a photometry error of 1.7 mJy by adding in quadrature the calibration uncertainty and the background noise. We measure a total flux density of 33.6 ± 1.7 mJy at 70 μm. Our flux value is consistent with the 70 μm flux measured by Engelbracht et al. (2008) of 34.9 ± 4.79 mJy.

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The Spitzer 160 μm map is confusion limited. The bulk of the emission is associated with sources outside the H i emitting region of I Zw 18. Although the Galactic latitude of I Zw 18 is ∼44°, it is possible that Galactic cirrus could be a significant source of confusion. We use the VLA H i observations to explore this possibility. Figure 2 shows the MIPS 160 μm and the SPIRE 250 μm map of a ∼5 × 5 arcmin field around I Zw 18. The thick lines represent the H i foreground emission from VLA. The thin lines represent the H i emission of I Zw 18. It is clear from visual inspection that the maxima of the H i foreground and the 160 and 250 μm emission are not coincident. We find a Pearson correlation coefficient close to zero. In most of the Spitzer confusion-limited images at 160 μm the confusion is mainly due to faint unresolved background sources (Dole et al. 2004). The bulk of the 160 μm emission, located southeast of our object, fragments into at least three point sources in the 250 μm map, which has finer spatial resolution. The 160 μm peak also coincides with several background galaxies in deep B- and R-band images (S. Janowiecki 2009, private communication). The difference between the 160 and 250 μm maps is consistent with what one would observe if the peak of the emission at 160 μm is associated with background galaxies.

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The background contamination and the absence of correlation between the 160/250 μm emission and the H i foreground emission make it impossible to recover the flux associated with I Zw 18. Thus, we use an annular sector around the galaxy to measure a 1σ surface brightness sensitivity of 0.18 mJy sr⁻¹ that includes the effects of confusion. We estimate the flux upper limit multiplying this value by the area associated with the 1.4 × 10²⁰ atom cm⁻² H i contour that encloses 96% of the 70 μm flux and 62% of the H i mass. To find the aperture correction factor associated with this area, we can approximate the contour using a circular aperture of 48'' radius. This corresponds to an aperture correction factor of 1.6 at 160 μm. After applying the aperture correction factor, we obtain a corresponding 3σ flux upper limit of 40.5 mJy. This new upper limit is a factor of ∼2 lower than the previous upper limit published by Engelbracht et al. (2008).

The Herschel PACS image at 160 μm also fails to detect I Zw 18. In this case, however, the image is not confusion limited. The 1σ surface brightness sensitivity is 1.8 MJy sr⁻¹. If we assume that the emission from I Zw 18 is compact on 12'' scales, the corresponding 3σ flux upper limit integrating over the 12'' beam and applying an aperture correction factor of 1.32 is 27.2 mJy.

We will work with the PACS 160 μm flux upper limit of 27.2 mJy for the rest of the paper. However, the upper limit measured from the PACS data relies on the assumption that the source is compact. If the 160 μm emission is significantly extended over scales larger than 12'' (∼1 kpc), it may be more appropriate to use the MIPS 160 μm upper limit of 40.5 mJy.

Finally, the SPIRE maps at 250, 350 and 500 μm show no detection of I Zw 18. From these images we measure a surface brightness sensitivity using an annular sector around the source. We then apply aperture corrections and point-source color corrections assuming β = 1.5 (β in f_ν∝ν^β) described in the SPIRE Photometry Cookbook.¹¹ We measure 3σ flux upper limits of 22.2, 23.9, and 25.4 mJy at 250, 350, and 500 μm, respectively.

We use two methods to estimate the dust mass of I Zw 18. In the first, we follow the procedure outlined by Hildebrand (1983), assuming an idealized graybody source with a single temperature. In the second, we use the Draine & Li (2007, hereafter DL07) model. The main difference between the DL07 model and the idealized graybody is that DL07 assume a grain size distribution that reproduces the observed wavelength-dependence extinction in the Milky Way and consequently a distribution of temperatures. Given the extreme nature of I Zw 18, it is not clear that either model is exactly applicable. Nonetheless, we used them so we can make a consistent comparison to larger samples of galaxies.

3.1.1. Modified Blackbody Model

For an idealized cloud, the dust mass is estimated by fitting its far-infrared spectrum as the product of a blackbody spectrum (B_{λ, T}) and a mass absorption coefficient (κ_λ). The absorption coefficient varies with wavelength as the negative power of the grain emissivity index (κ_λ∝λ^−β, where β represents the emissivity index). Then, for a cloud that is optically thick to starlight and optically thin to far-infrared emission, the dust mass M_Dust is given by the following expression:

$$\begin{equation} M_{{\rm Dust}} = \frac{F_{\lambda }D^{2}}{\kappa _{\lambda }B_{\lambda ,T}}{,} \end{equation} \tag{ 1 }$$

where D is the distance to the galaxy, F_λ is the observed flux, and B_{λ, T} is the blackbody intensity. The flux at any point on a graybody spectrum is F_λ∝B_{λ, T}λ^−β, with β independent of wavelength. Therefore, we can solve for the color temperature (T_70/160) using the ratio F₇₀/F₁₆₀.

Measured values for κ_λ at 250 μm (κ₂₅₀) span the range ≈5–15 cm² g⁻¹ (Alton et al. 2004), and commonly used values for β are 1–2 depending on the environment. For this work we adopt κ₂₅₀  = 9.5 cm² g⁻¹ and β = 1.5; these are commonly used values for low-metallicity galaxies (e.g., Leroy et al. 2007a). Using β = 1 or 2 changes our dust mass limits by ∼10%.

Figure 3 shows the spectral energy distribution (SED) of I Zw 18. The source is only detected at 70 μm. At longer wavelengths each point corresponds to a 3σ flux upper limit. Among these limits, the 160 μm upper limit represents the strongest constraint on the I Zw 18 SED. Thus, based on the 70 and 160 μm emission, the modified blackbody spectrum model constrains the dust temperature to be T_70/160 > 33.7 K. This translates into a predicted 850 μm flux of 0.28 mJy, compatible with the observed upper limit of 1.25 mJy (Galametz et al. 2011). Combining our temperature lower limit with the 70 μm flux, Equation (1) yields a dust mass of M_Dust < 3.2 × 10³ M_☉. If we use the MIPS 160 μm upper limit instead of the PACS upper limit, we measure a temperature limit T_70/160 > 29.8 K and a dust mass a factor of ∼2 higher, i.e., M_Dust < 6.9 × 10³ M_☉.

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3.1.2. Draine and Li Model

The DL07 dust mass upper limit is a factor of ∼3.5 larger than the dust mass estimated using the modified blackbody model. The DL07 model treats dust emission as an ensemble of dust grains at different temperatures that includes larger masses of dust at colder temperatures than what is predicted by the single-temperature fit. Therefore, it is not surprising that this model generates a higher dust mass than the modified blackbody model. However, the fact that these two measurements are not extremely different increases our confidence in the dust mass limit, which we conservatively take to be that resulting from the DL07 model.

It is interesting to compare this result to other modeling efforts for I Zw 18 and low-metallicity galaxies. In particular, Galametz et al. (2011) determine dust masses in a large sample of galaxies with literature data, using full SED modeling based on the Zubko et al. (2004) grain model. They find that the inclusion of submillimeter-wave data tends to drive dusty galaxies toward lower dust masses, while for low-metallicity galaxies the inclusion of submillimeter-wave constraints yields higher dust mass predictions than those from far-infrared alone. By contrast, Draine et al. (2007) found their masses to be robust to the inclusion of submillimeter-wave data. This is in part driven by modeling choices, in particular the inclusion of a minimum radiation field or the interpretation of submillimeter-wave excess (Israel et al. 2010; Bot et al. 2010) as caused by cold dust. The latter appears to be associated with low metallicities, and although recent studies suggest that it is not caused by cold dust (Galliano et al. 2011), it remains a large systematic uncertainty in dust mass determinations. Also note that for dwarf galaxies the SCUBA data included by Galametz et al. (2011) are much deeper than those used by Draine et al. (2007). Observational biases and limitations have a non-negligible impact on the interpretation of the observed trends in dust-to-gas ratio versus metallicity.

Galametz et al. (2011) use a 160 μm flux upper limit of 76.8 mJy (Engelbracht et al. 2008). For submillimeter-wave data they use an 850 μm flux upper limit of 1.25 mJy (Galliano et al. 2008). They measure an upper limit to the dust mass of 1.1 × 10⁵ M_☉ scaled to our adopted distance. Our dust mass upper limit is an order of magnitude smaller than that of Galametz et al. (2011). Using the DL07 model and the data in Galametz et al. (2011), we would obtain an upper limit of 1.0 × 10⁵ M_☉. This is nearly equivalent to the dust mass Galametz et al. (2011) find, highlighting the fact that the mass limits are likely reasonably robust to the choice of models. Therefore, our lower dust mass limit is due to the tighter flux limits at 160 μm.

The total H i mass of I Zw 18 is M_H i = 2.3 × 10⁸ M_☉ (van Zee et al. 1998). The molecular content of I Zw 18, however, remains unknown since no CO emission has been detected. Our new upper limit on the CO J = 1 → 0 luminosity of I Zw 18 is L_CO ⩽ 10⁵ K km s⁻¹ pc² (4σ), which corresponds to M_H2 ⩽ 450,000 M_☉ for a standard conversion factor (α_CO = 4.5 M_☉ (K km s⁻¹ pc²)⁻¹). Note that our luminosity is similar to that quoted by Leroy et al. (2007b) because we adopt here a larger distance (for matched smoothing and assumptions we improve the sensitivity of that study by a factor of two). Using this Milky-Way-based conversion factor, M_H2 is at most 0.2% of the total gas mass.

There is no reason to expect that the Milky-Way-based conversion factor between CO luminosity and H₂ mass applies to low-metallicity galaxies like I Zw 18. In the Local Group, α_CO is a strong function of metallicity (Leroy et al. 2011). Genzel et al. (2012) derive a correlation between oxygen abundance and conversion factor, α_CO. Applying their formula to a galaxy with the metallicity of I Zw 18, we find a conversion factor α_CO ≈ 477.5 M_☉ (K km s⁻¹ pc²)⁻¹. This factor is ∼100 times larger than α_CO in a typical spiral galaxy. Using this conversion factor, we calculate a molecular gas mass upper limit of M_H2 ⩽ 4.8 × 10⁷ M_☉. This M_H2 is ∼20% of the total gas mass.

There is some evidence that, at low metallicities, the star formation activity may be a better indicator of the molecular mass than the CO emission (Krumholz et al. 2011; Bolatto et al. 2011; Schruba et al. 2011). The Hα flux of I Zw 18 suggests a recent star formation rate (SFR) of ∼0.1 M_☉ yr⁻¹. In large star-forming galaxies, a typical H₂-to-SFR ratio (H₂ depletion time) is ∼1–2 Gyr (Bigiel et al. 2011). The H₂ mass corresponding to this amount of star formation in such a galaxy would thus be ∼10⁸ M_☉. Given the level at which star formation obviously dominates the morphology and ISM conditions in I Zw 18, we strongly suspect that this kind of equilibrium assumption very much overestimates the H₂, which will have been dissociated or otherwise destroyed by the recent burst. Nonetheless, even in this limit the H₂ only makes up ∼30% of the integrated gas mass. The similarity with the results obtained from applying the Genzel et al. (2012) correlation is not surprising, since the underlying assumption is the same. Because of its uncertainty, we do not include the H₂ correction in the following calculations.

Draine et al. (2007) find that the DGR changes significantly depending on whether the dust mass is compared to the total gas mass or only the gas mass enclosed in the aperture where the infrared emission is measured. For example, for IC 2574 (a dwarf galaxy in the SINGS sample), only 19% of the H i gas mass is enclosed in the area where the infrared emission is detected (Walter et al. 2007). We take the point of view that these are two valid definitions of the DGR: global, or local where the dust emission is detected. Using the total H i mass from van Zee et al. (1998), we measure an upper limit for the global DGR ≲  5 × 10⁻⁵. Using instead the H i mass enclosed in the area were we measure the 160 μm flux upper limit (62% of the total H i mass) yields a local DGR ≲  8.1 × 10⁻⁵.

Figure 4 shows the DGR as a function of oxygen abundance for I Zw 18 and a subsample of SINGS galaxies. Open symbols indicate 3σ upper limits. The solid line represents a linear scaling of the DGR with metallicity. This linear relation assumes that the abundances of all heavy elements are proportional to the oxygen abundance and that the same fraction of all heavy elements are in solid form as in the Milky Way (Draine et al. 2007). The I Zw 18 DGR upper limit is primarily driven by the upper limit in the dust mass, while in the SINGS galaxies the upper limits are due to lower limits in the gas mass (due to the non-inclusion of H₂). As we discussed in Section 3.1, we obtain different dust masses for I Zw 18 depending on the assumption we make about the distribution of the 160 μm emission (point-like with PACS and extended with MIPS). The open star shows the DGR of I Zw 18 when we assume point-like emission, while the upper limit of the bar shows the DGR when we assume extended emission. For the SINGS galaxies, the dust and gas masses are from Draine et al. (2007) and the metallicities are from Moustakas et al. (2010). Note that Draine et al. (2007) compute molecular gas masses assuming a fixed X_CO factor of 4 × 10²⁰ cm⁻² (K km s⁻¹)⁻¹ following Blitz et al. (2007). We show SINGS galaxies with and without measured SCUBA fluxes as triangles and circles, respectively, as Draine et al. (2007) find that the dust mass estimates with and without SCUBA data can differ by a factor of ∼2.

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The left panel of Figure 4 shows the global DGR, estimated using the total gas masses. The right panel shows how the DGR changes when estimating it locally in low-metallicity systems, including I Zw 18, by using the gas mass enclosed in the region where the infrared emission is detected. For SINGS galaxies with metallicities 12+log(O/H) ≳ 8.1, the total DGR seems to agree within a factor of ∼2 with a linear relationship between DGR and metallicity. Low-metallicity galaxies do not seem to follow the same linear correlation that includes the Milky Way DGR. The I Zw 18 global DGR falls below the linear scaling by a factor of ∼8. The right panel of Figure 4 shows the local DGR. The DGRs of the SINGS low-metallicity systems scale up and appear consistent with the linear relationship within a factor of ∼2, although most of the low-metallicity points are only upper limits. For I Zw 18, however, the local DGR falls below the linear scaling by a factor of ∼5. Therefore, our dust mass limits for I Zw 18 suggest a breakdown of the linear relationship between DGR and metallicity at very low metallicities. Note further that, at least in terms of the global DGR, I Zw 18 seems to continue the trend found for other low-metallicity galaxies.

We show in Figure 4 that only one of the seven SINGS galaxies with 12+log(O/H) ≲ 8.1 has a DGR that is not an upper limit. It may be possible that the local DGR of this system is higher than other low-metallicity galaxies and the trend is really steeper than linear, as our result for I Zw 18 and other studies suggest (Lisenfeld & Ferrara 1998; Muñoz-Mateos et al. 2009). Clearly more work is needed to determine, robustly, whether low-metallicity galaxies do or do not follow the linear scaling shown in Figure 4.

Note that the abundance of oxygen may not be the correct abundance to refer to. Indeed, the abundances of refractory elements that constitute the bulk of the dust such as carbon or silicon are likely more relevant to establishing the DGR. Garnett et al. (1999), for example, find a trend of increasing C/O with O/H for a sample of irregular and spiral galaxies observed with HST. This could suggest that the nonlinear trend of DGR with metallicity is really an artifact of using O/H as a proxy for metallicity, and the relation could become more nearly linear when plotted against C/H. Garnett et al. (1999) find a gas-phase abundance of C in I Zw 18 that is significantly higher than that predicted by the extrapolation of the observed C/O versus O/H trend in low-metallicity irregular galaxies. In fact, C/O in I Zw 18 is only 0.3 dex lower than solar. This is barely enough to reconcile our limits on the local DGR with a linear trend with C/H, and probably not enough to explain our low global DGR, but it certainly goes in the right direction.