The dust content of the most metal-poor galaxies

The dust content of the most metal-poor star-forming galaxies

Raffaella Schneider, Leslie Hunt and Rosa Valiante
INAF/Osservatorio Astronomico di Roma, Via di Frascati 33, 00040 Monte Porzio Catone, Italy
INAF/Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, 50125 Firenze, Italy
draft version 20 November 2015

Although dust content is usually assumed to depend uniquely on metallicity, recent observations of two extremely metal-poor dwarf galaxies have suggested that this may not always be true. At a similar oxygen abundance of 3% , the dust-to-gas and dust-to-stellar mass ratios in SBS 0335052 and I Zw 18 differ by a factor 40-70 according to including molecular gas or excluding it. Here we investigate a possible reason for this dramatic difference through models based on a semi-analytical formulation of chemical evolution including dust. Results suggest that the greater dust mass in SBS 0335052 is due to the more efficient grain growth allowed by the high density in the cold interstellar medium (ISM), observationally inferred to be almost 20 times higher than in I Zw 18. Our models are able to explain the difference in dust masses, suggesting that efficient dust formation and dust content in galaxies, including those with the highest measured redshifts, depend sensitively on the ISM density, rather than only on metallicity.

ISM: abundances — ISM: evolution — galaxies: starburst — galaxies: dwarf — galaxies: evolution — galaxies: individual: SBS0335-052 — galaxies: individual: IZw18
pagerange: The dust content of the most metal-poor star-forming galaxiesReferencespubyear: 2015

1 Introduction

The dust content in galaxies is intimately linked to their evolutionary history. Nevertheless, the mass of the dust in the interstellar medium (ISM), and its ratio with the gas mass (dust-to-gas ratio, DGR), are critical parameters for establishing the evolutionary state of a galaxy. However, the complex interplay between dust destruction and dust formation mechanisms (e.g., Dwek, 1998; Bianchi & Schneider, 2007; Jones & Nuth, 2011), makes it difficult to infer evolutionary trends from dust alone.

Another signature of evolutionary status is a galaxy’s metal abundance, generally quantified by the nebular abundance of oxygen, O/H. Although dust grains consist mainly of metals, grains are not the dominant contributor to the metal budget of galaxies (Peeples et al., 2014). Nevertheless, the metals in dust and the metals in gas are expected to be coupled through the ISM energy cycle, and much work has been focused on comparing dust content with metallicity. Indeed, the DGR and O/H seem to be fairly well correlated both in the Milky Way and in nearby star-forming galaxies. Observations of the DGR compared with the gas-phase metallicity suggest approximate linearity between the two (e.g., Issa et al., 1990; Schmidt & Boller, 1993; Draine et al., 2007), a trend which is generally true even for gradients of the DGR within galaxies, which tend to follow the radial changes in metallicity (e.g., Muñoz-Mateos et al., 2009; Magrini et al., 2011). Since the seminal work by Dwek (1998), many galaxy evolution models and models of the ISM now assume that dust content is proportional to metallicity (e.g., Granato et al., 2000; Wolfire et al., 2003; Gnedin et al., 2009; Krumholz et al., 2009b). In the ISM models, this assumption is directly related to the capability of the gas to self-shield from intense ultraviolet radiation, and is thus crucial for the formation of H.

However, new results with Herschel and ALMA challenge the assumption of a direct (linear) correspondence of the DGR with metal abundance. Based on dust masses calculated with Herschel data from the Dwarf Galaxy Survey (Madden et al., 2013), Rémy-Ruyer et al. (2014) found that the DGR is linearly proportional to O/H only to 12log(O/H)8 (20% ); at lower metallicities the dependence of DGR is steeper, implying relatively less dust (or more gas) at lower abundances. By including new ALMA data at 870 µm, Hunt et al. (2014, hereafter H14) derive vastly different DGRs even at the same metallicity, in particular for the two most metal-poor star-forming galaxies in the Local Universe, SBS 0335052 and I Zw 18, both at 3% . As shown in Fig. 1 (adapted from Hunt et al. 2014, see also Sects. 2.12.3) the DGRs of these two galaxies differ by almost two orders of magnitude, despite their similar metallicity.

In this paper, we examine possible reasons for this dramatic difference in dust content at similar metallicity in these two galaxies. We first discuss their basic properties in Sect. 2. Then, in Sect. 3, we explore the origin of the observed dust in SBS 0335052 and I Zw 18 using a semi-analytic chemical evolution model with dust. The model has been first introduced by Valiante et al. (2009) and then applied by Valiante et al. (2011, 2012, 2014) and de Bennassuti et al. (2014) within the context of a hierarchical model for the evolution of cosmic structures, as predicted by the concordance CDM model. Here we do not investigate the hierarchical evolution of SBS 0335052 and I Zw 18, but rather limit the discussion to their chemical evolution assuming that they evolve in isolation with a constant star formation rate (SFR)111This assumption is almost certainly inexact, but provides a benchmark for our assessment of consistency with observations.. Below, we only briefly describe the model, referring interested readers to the above papers for a more detailed description. We discuss implications of our results for high-redshift dust formation in star-forming galaxies in Sect. 4, and our conclusions are given in Sect. 5.

2 Observed properties of I Zw 18 and SBS 0335052

The observed properties of the two metal-poor dwarf galaxies that we have adopted for our analysis are presented in Table 1. The observational data and the methods used to infer the physical properties listed in the table have been thoroughly described in H14 and references therein (see in particular Tables 1 and 3 in H14). H14 analyzed dust and gas surface densities and did not include ionized gas. Here we revise the estimates of gas masses in both galaxies relative to H14 in order to take into account the ionized gas component and the spatial extent of cool dust emission. The values obtained for the individual ISM components and the total gas masses are given in Table 1 and shown graphically in Fig. 1.

2.1 Atomic gas masses

Both I Zw 18 and SBS 0335052 are embedded in vast Hi envelopes which include other galaxies or galaxy components. SBS 0335052 has a western component SBS 0335052W at a distance of 22 kpc within a 64 kpc Hi cloud (Pustilnik et al., 2001; Ekta et al., 2009); I Zw 18 (main body) lies about 2 kpc away from the “C” component, or Zwicky’s flare, within a diffuse Hi cloud extending over 19 kpc (van Zee et al., 1998; Lelli et al., 2012). Thus it is difficult to determine exactly where the Hi of the galaxy ends, and the more extended Hi envelope begins. The large beams with which Hi is typically observed exacerbate the problem, both because of beam dilution which causes Hi surface density to be underestimated, but also because the tiny dimensions of the galaxies compared with their Hi envelope make it difficult to assess the Hi content of the galaxy itself.

Because our interest here is in dust production, and in the cool gas reservoir that provides the fuel for star formation, we have taken Hi surface densities from the highest-resolution observations available (as in H14), and calculated Hi mass over the optical extent of the galaxy as determined from (-band) surface-brightness profiles. The -band brightness profile of I Zw 18 falls to 25 mag arcsec at a radius of 8 arcsec (700 pc, Hunt et al., 2003), and a radius 32 for SBS 0335052 (838 pc, Thuan et al., 1997). With mean Hi surface densities  = 56  pc for SBS 0335052 (Thuan & Izotov, 1997) and 64  pc for I Zw 18 (Lelli et al., 2012), we thus estimate total Hi masses of 3.1 and 2.5 for SBS 0335052 and I Zw 18, respectively. The Hi mass for SBS 0335052 is about 10 times lower than the total Hi mass by Ekta et al. (2009) in a 40 arcsec beam (about 6 times larger than the optical extent of the galaxy), and 4 times lower than the total for I Zw 18 given by Lelli et al. (2012). Using the total Hi masses from the literature would lower the resulting DGR by roughly these amounts (e.g., Rémy-Ruyer et al., 2014).

Figure 1: Dust-to-gas mass ratios (DGRs) as a function of metallicity. Filled (blue) circles show DGRs inferred from the total gas mass of SBS 0335052 and I Zw 18, including ionized gas, atomic and (putative, as yet undetected) molecular gas; open circles give DGRs including only the ionized and atomic gas components. Galaxies from Galametz et al. (2011) are shown as (green) open stars, those from Draine et al. (2007) as (red) crosses, and from Leroy et al. (2011) as (magenta) open circles. The short dashed line is the linear prediction by Draine et al. (2007), and the vertical dotted line illustrates solar metallicity 12log(O/H) = 8.69 (Asplund et al., 2009). The long dashed line (starting at 12log(O/H) = 8.0) is the empirical fit given by Rémy-Ruyer et al. (2014) for low metallicities.

2.2 Ionized gas masses

In low-metallicity star-forming galaxies such as I Zw 18 and SBS 0335052, ionized gas constitutes an important part of the total gas mass budget. Hence, we have attempted to determine the mass of the ionized component in the two galaxies.

Radio continuum observations of the free-free emission of ionized gas give emission measures, and thus mean densities and source size. The radio spectrum for I Zw 18 is flat, consistent with optically thin emission (Cannon et al., 2005; Hunt et al., 2005b), while that of SBS 0335052 falls at low frequency, indicative of free-free absorption and consequently high ionized-gas density (Hunt et al., 2004; Johnson et al., 2009). As discussed in detail in Sect. 2.6, the density of ionized gas in I Zw 18 is 5 cm, and 3200 cm in SBS 0335052, corresponding to emitting regions of 390 pc radius for I Zw 18 (Hunt et al., 2005b) and 7.7 pc radius for SBS 0335052 (Johnson et al., 2009).

Because ionized gas tends to be clumped (Kassim et al., 1989; Kennicutt, 1984; Zaritsky et al., 1994; Martin, 1997; Giammanco et al., 2004; Cormier et al., 2012; Lebouteiller et al., 2012), we need to estimate a volume filling factor over the optical extent of the galaxy. We have done this by comparing the source size inferred from the radio emission measure to the optical size (see Sect. 2.1), assuming a spherical geometry for the Hii region. This comparison gives a volume filling factor of 0.17 for I Zw 18 and for SBS 0335052. Although the value for I Zw 18 is within those observed for local Hii regions (e.g., Kassim et al., 1989), the value for SBS 0335052 is extremely low. This could be a consequence (e.g., Giammanco et al., 2004) of the optically thick gas in this galaxy as indicated by the radio spectrum, so for SBS 0335052 we have used conservatively a filling factor of , roughly the lowest value found by Martin (1997). With these densities and filling factors, and the optical size of the galaxy as for Hi, we estimate ionized gas masses of  and  for I Zw 18 and SBS 0335052, respectively. The mass of the ionized gas is comparable to that of the atomic gas in both galaxies.

If, instead of the radio-determined value of 3200 cm, we consider the ionized gas density of 500 cm for SBS 0335052 inferred from the optical [S ii] lines (Izotov et al., 1999), and a larger filling factor of , we would estimate an ionized gas density of , 50% of our former estimate. This can be considered as a rough measure of the uncertainty inherent in this calculation.

2.3 Molecular gas masses

CO emission has never been detected in either galaxy; thus it is difficult to measure H masses, independently of the unknown CO luminosity-to-H mass conversion factor . Thus, H14 measured the distance from the gas scaling relations in order to estimate the missing (undetected) H gas surface density (for more details, see H14). Using the densities from H14 ( =94  pc and  = 342  pc, for I Zw 18 and SBS 0335052, respectively) and the optical size of the galaxy as above, we infer H masses for I Zw 18 and SBS 0335052 of  and , respectively. These masses are highly uncertain, and assume that SFR surface density at low metallicity follows the same scaling relations as more metal-enriched galaxies.

2.4 Dust masses and comparison with previous work

Dust masses for SBS 0335052 and I Zw 18 were measured by H14 by fitting the optical-to-mm spectral energy distributions (SEDs) with spherical DUSTY models (Ivezic & Elitzur, 1997). Three different grain populations were included for determination of the best-fit model (for more details see H14). The resulting dust masses for both galaxies differ from those measured by other groups (e.g., Rémy-Ruyer et al., 2013; Fisher et al., 2014; Rémy-Ruyer et al., 2014; Izotov et al., 2014). H14 discussed differences relative to Rémy-Ruyer et al. (2013) for SBS 0335052 and Fisher et al. (2014) for I Zw 18; here we compare our measurements to more recent work although we are unable to compare our dust-mass estimates with Rémy-Ruyer et al. (2014) because there is no tabulation of their dust masses.

Izotov et al. (2014) use a multiple-temperature modified blackbody (MBB) approach, and fix the emissivity index for all components. However, they only discuss the warm and cold dust (not the hot) because, as they note, the hot dust (for m) is not in thermal equilibrium. Considering their two-component fits, the SEDs shown in their Fig. 6 almost never pass through the longer wavelength points. This is a consequence of the assumption of single-temperature MBBs, and is expected to bias dust-mass estimates toward lower masses. Although seemingly a small deviation, the constraints offered by longer wavelengths significantly raise dust mass estimates, especially at low metallicity (e.g., Galametz et al., 2011). It is well known that including short wavelengths in a single-temperature MBB fit gives unrealistically low dust masses because the mean temperature of the dust radiating at these short wavelengths is higher than the bulk of the cooler dust which dominates the mass. The warm dust dominates the light but the cool dust dominates the mass and a single temperature (or even two temperatures as in Izotov et al., 2014) are not able to accommodate the temperature gradients.

The cold-dust mass found by Izotov et al. (2014) for I Zw 18 is 70% of that found by H14; compensating for the differences in dust emissivities worsens slightly the discrepancy to 65%. This value is also a factor of 2 below the lower limit of the range of dust mass estimated for I Zw 18 by Fisher et al. (2014) who use models by Draine & Li (2007), even after compensating for the different emissivities adopted by the two groups. More physically realistic models which contemplate dust temperature gradients through variations in the interstellar radiation field that heats the dust tend to give larger dust masses than single-temperature MBB fits.

For SBS 0335052, Izotov et al. (2014) find a cold dust mass of dex 3.06 , roughly a factor of 30 below H14. However, they estimate a “cold” temperature of 57 K, very close to the temperature of 59 K discussed by H14 under the assumption of single-temperature dust, and thus do not take into account any cool dust. Moreover, the dust in SBS 0335052 is optically thick at short wavelengths (Thuan et al., 1999; Plante & Sauvage, 2002; Houck et al., 2004; Hunt et al., 2005a; Hunt et al., 2014); thus the assumption of optically thin dust emission implicit in MBB fitting is incorrect.

The differences found in dust masses for SBS 0335052 and I Zw 18 of roughly a factor of 100 are consistent with the differences in their integrated IR luminosity: for SBS 0335052 is , while for I Zw 18  = . Assuming the same mass-to-light ratio (similar overall mean temperatures) for the dust, this would give a factor of 80 in dust mass, inconsistent with the difference found by Izotov et al. (2014) of roughly a factor of 5 for the cold dust masses in the two galaxies. This illustrates one of the difficulties of the MBB approach adopted by Izotov et al. (2014); they use two temperatures and thus apply two different mass-to-light ratios (roughly inverse temperature) to the two IR integrals. As mentioned above, in galaxies like SBS 0335052 and I Zw 18 most of the dust emission comes from warm dust, while most of the dust mass is cold.

More emissive grain mixtures, as suggested by Jones et al. (2013), would decrease the inferred dust mass by a factor 3-4 in both galaxies. A comparable reduction of the dust mass of SBS 0335052 () would be obtained by artificially imposing a low 870 µm dust flux (1 below the reported H14 flux).

We will discuss the implication of this reduction in dust mass for our results in Sect. 3.

Figure 1 shows the DGRs of I Zw 18 and SBS 0335052, together with samples of galaxies taken from the literature (with dust masses obtained through SED fitting rather than MBB approximations). Because the dust-mass estimates for these samples are based on the Draine & Li (2007) models, the dust emissivities are comparable among the samples. Figure 1 also shows the steeper-than-linear slope found by Rémy-Ruyer et al. (2014) for galaxies with oxygen abundance 12log(O/H)8.0. The DGR of SBS 0335052 is roughly consistent with a linear slope of DGR with O/H (e.g., Draine et al., 2007), while I Zw 18 follows the steeper slope found by Rémy-Ruyer et al. (2014).

Name Distance Gas SFR Age 12
(Mpc) Component () ) ( yr) (Myr) Log(O/H) () () () ()
I Zw 18 18.2 Ionized 3.07
Atomic 2.46
Molecular 3.62
Total 9.15 1.02 (1.82) 0.17 (0.10) 6 (18.3) 7.18 3.09 (2) 100 10
SBS 0335052 54.1 Ionized 5.85
Atomic 3.09
Molecular 18.9
Total 27.8 7.92 (23.5) 1.32 (1.79) 6 (13.1) 7.27 3.80 (2) 1500 80
Table 1: Adopted physical properties of the two galaxies. The SFR values are from radio-continuum SED fitting. The stellar ages are the mean values of stellar clusters and the stellar masses have been derived integrating the SFR over the mean ages (see text). The values in parentheses correspond to those from DUSTY SED fitting (stellar mass, stellar age, metallicity, dust mass) and to a constant SFR inferred from the DUSTY SED best-fit stellar mass and ages.

2.5 Stellar masses, stellar ages, and SFR

Stellar masses in star-forming dwarf galaxies such as SBS 0335052 and I Zw 18 are notoriously difficult to determine. The main problem is contamination by nebular continuum emission which affects both the optical (e.g., Reines et al., 2008, 2010; Adamo et al., 2010) and the near-infrared emission (e.g., Smith & Hancock, 2009; Hunt et al., 2012). In SBS 0335052, the contamination from free-free emission at 3.4 µm is 27% (Hunt et al., 2001) and 50% at 2.2 µm (Vanzi et al., 2000); even more extreme contamination is observed in I Zw 18, with 50% of the IRAC 4.5 µm flux due to nebular emission (Hunt et al., 2012). Hot dust is also a problem, especially in SBS 0335052 where it comprises 67% of its 4 µm emission (Hunt et al., 2001). While nebular continuum levels can be estimated from SFRs (e.g., Smith & Hancock, 2009; Hunt et al., 2012), it is difficult to ascertain hot-dust levels without detailed multi-wavelength photometry. Thus stellar masses of low-metallicity dwarf starbursts such as SBS 0335052 and I Zw 18 are prone to large uncertainties.

Table 1 reports in parentheses the values of stellar mass, M, and age inferred from DUSTY SED fitting (H14), and SFRs that correspond to the constant values needed to produce the DUSTY SED best-fit Mwhen integrated over the best-fit age. However, for our analysis, we require a mean age for the stellar populations producing the dust currently observed. A mean age of stellar clusters of 6 Myr has been calculated by averaging values from Recchi et al. (2002) and Hunt et al. (2003) for I Zw 18 and from Reines et al. (2008) for SBS 0335052. Thus, we have also computed the stellar mass accumulated over the timespan of the mean ages of the clusters at a constant rate given by the observed values of SFR derived from radio free-free emission (Hunt et al., 2005b; Johnson et al., 2009). All these values (not in parentheses) are also reported in Table 1.

The resulting M values are within 40% of previous estimates obtained by fitting the optical-NIR SEDs of individual star clusters with single stellar population models (SBS 0335052: , I Zw 18: , Reines et al., 2008; Fumagalli et al., 2010, respectively).

Only if age priors (3-6 Myr) are imposed for the fit are the DUSTY stellar masses obtained by H14 consistent with these values for SBS 0335052. There is a similar discrepancy for the DUSTY stellar mass of I Zw 18 at an age of 18.3 Myr, almost a factor 2 larger than the value obtained with a constant SFR of 0.17  yr. Part of the reason for this is that, at a given luminosity, the mass-to-light ratios are smaller for younger stellar populations (see H14 for details). Another reason is that there is an age gradient in both galaxies, and the SED fitting relies on global photometry that encompasses both young and old clusters. In SBS 0335052, the northern super-star clusters (SSCs) are older with a maximum age of 12 Myr, compared to 3 Myr for the southern ones (Reines et al., 2008; Adamo et al., 2010); in I Zw 18, the SE cluster and C component are older ( Myr) compared to the younger NW cluster (3 Myr, Hunt et al., 2003).

Such a difference in the stellar ages can have important implications for the chemical evolution of the system. In Fig. 2 we show the stellar mass-lifetime relation for stars with initial metallicity  = 0.03, using the Raiteri et al. (1996) formulation. The shaded regions illustrate the ranges of stellar masses that contribute to metal enrichment by means of core-collapse SN explosions and stellar winds from intermediate mass stars. The vertical grey lines indicate the values of stellar ages shown in the table (dashed lines are the DUSTY stellar ages). The figure shows that part of the metals and dust that we presently observe may have originated in situ, from supernova explosions (self-enrichment scenario). However, if we adopt the mean age of the stellar clusters (solid line), only the most massive supernovae with 34  40   have evolved to their metal production stage. Hence the ISM of the galaxies must have achieved most of its metal content prior to the current star-formation episode (pre-enrichment scenario). If, instead, the stellar population age for SBS 0335052  (I Zw 18) is 13.1 Myr (18.3 Myr), as inferred from DUSTY SED fit, then the mass range of the stars that can contribute to the ISM enrichment extends to 16  40   (13  40 ).

Fig. 3 quantifies this difference in terms of the mass of metals and dust that can be produced by self-enrichment. It shows that – depending on the adopted stellar age – the mass fraction of metals (dust) relative to the stellar mass is in the range () for SBS 0335052  and in the range () for I Zw 18. Using the corresponding stellar masses reported in Table 1, we find that – even assuming that all the newly formed dust injected in the ISM is conserved – the dust mass produced by self-enrichment is always smaller than observed, being for SBS 0335052  and for I Zw 18. As explained below, these values have been obtained using the dust and metal yields presented by Valiante et al. (2009) and assuming that the stars form at a constant rate with a Salpeter Initial Mass Function (IMF) in a mass range 0.1  100   with a metallicity of .

Figure 2: The dependence of the stellar lifetime on the initial stellar mass for stars with metallicity  = 0.03 (solid black line). The orange and blue regions indicate the progenitor mass ranges of core-collapse SN and AGB stars, respectively. The solid and dashed vertical lines indicate the estimated stellar ages for the two galaxies, based on individual super stellar clusters fits and on DUSTY SED fits, respectively (see text).
Figure 3: The mass fraction of metals (dark green) and dust (red) relative to the mass of stars as a function of the stellar age. The solid and dashed vertical lines indicate the estimated stellar ages for the two galaxies, based on individual super stellar clusters fits and on DUSTY SED fits, respectively (see text).

2.6 Cold gas densities and temperatures

The remaining quantities required for our models are the mean density and temperature of the cold neutral medium (CNM) and molecular clouds in which dust grains form and grow by accretion (see Sect. 3). We can derive the number densities of the molecular phase by assuming thermal pressure balance at the atomic-molecular interface (e.g., Krumholz et al., 2009a). Observationally and from a theoretical point of view, the mean number density of molecular clouds, , is expected to be times that in the CNM of the ISM:  = . We can therefore calculate approximate values of in SBS 0335052 and I Zw 18 by first considering the observed Hi column densities222We have considered regions of similar size, constrained by requiring a similar physical resolution of the Hi observations: 524 pc (2″) for SBS 0335052 and 436 pc (5″) for I Zw 18.: cm and cm for SBS 0335052 and I Zw 18, respectively (Thuan & Izotov, 1997; Lelli et al., 2012). These can be converted to mean volume densities over the regions of interest (the area subtended by the massive star clusters) by considering the diameters of the star-forming region: 15.8 pc for SBS 0335052 (Johnson et al., 2009) and 170 pc for I Zw 18 (Cannon et al., 2002; Hunt & Hirashita, 2009). We thus obtain a mean molecular density 1435 cm  and 91 cm for SBS 0335052 and I Zw 18, respectively.

Despite the similar metallicities of the two galaxies, the inferred molecular densities differ by more than an order of magnitude. Nevertheless, these estimates are roughly consistent, given the uncertainties, with the densities that would be inferred from the putative (unobserved) molecular component discussed by H14. Assuming that the Kennicutt-Schmidt law relating gas and star-formation surface densities holds also for these two galaxies, and with the same sizes as above, we would derive 1800 cm for SBS 0335052 and 40 cm for I Zw 18. The radio spectrum also shows evidence for such a difference in gas densities in the two galaxies. While in SBS 0335052 there is the clear signature of a strongly absorbed thermal component, both globally (Hunt et al., 2004) and around the individual southern SSCs (Johnson et al., 2009), I Zw 18 shows a typical flat bremßtrahlung spectrum (Hunt et al., 2005b). Based on fits of the radio spectrum, the ionized-gas densities inferred for the two objects are 3200 cm for SBS 0335052 (Johnson et al., 2009), and 10 cm for I Zw 18 (Hunt et al., 2005b). Finally, even the optical spectra of the two objects show a large difference in the densities measured from the [Sii] lines: 500 cm for SBS 0335052 and 100 cm for I Zw 18 (Izotov et al., 1999). Given the uncertainties in the above estimates, in what follows we take the reference values of 1500 cm and 100 cm for the molecular gas densities in SBS 0335052 and I Zw 18, respectively.

Following Krumholz et al. (2009a), we can use the temperature-density relation for the CNM predicted by Wolfire et al. (2003) ISM model333We have considered the most general expression for the CNM temperature, which takes into account the vastly different DGRs for these two galaxies. to find and then derive the temperature of the molecular gas implied by thermal pressure balance, . The resulting values for the two galaxies are shown in Table 1.

3 The chemical evolution model

The equations describing the chemical evolution of a galaxy that evolves in isolation (closed-box approximation), can be summarized as follows:


where is the stellar mass, is the total mass in the ISM (the sum of the gas and dust masses), is the total mass in heavy elements (both in the gas phase and in dust grains), is the dust mass (so that the mass of gas phase elements is given by ), is the ISM metallicity, and is the total dust abundance in the ISM. The terms , and are the rates at which the mass of gas, heavy elements and dust is returned to the ISM after stellar evolution, respectively. These time-dependent terms depend on the adopted model grids and stellar IMF. We compute them as follows:


where the lower limit of integration, , is the mass of a star with a lifetime ; and are respectively the remnant mass, the metal and dust mass yields, which depend on the stellar mass and metallicity; and is the stellar IMF, which we assume to be a Salpeter law in the mass range 0.1  100  (e.g., Valiante et al., 2009). For stars with , we adopt metal yields from van den Hoek & Groenewegen (1997) and dust yields for intermediate-mass stars on the AGB phase of the evolution by Zhukovska et al. (2008). For massive stars (12  40 ) metal and dust yields have been taken from Woosley & Weaver (1995) and from Bianchi & Schneider (2007), using the proper mass-and metallicity-dependent values and including the effect of the reverse shock on dust survival in SN ejecta. For stars in the intermediate mass range 8  12  , we interpolate between the AGB yields for the largest-mass progenitor and SN yields from the lowest-mass progenitor. Above 40 , stars are assumed to collapse to black hole without contributing to the enrichment of the ISM. Finally, the last two terms in the right-hand side of eq. (3) represent the effects of dust destruction by interstellar shock waves and grain growth in the dense phase of the ISM. Here we simplify the treatment of the two-phase ISM model described in de Bennassuti et al. (2014), and quantify the fraction of ISM in the cold phase with the parameter . This is taken to be time-dependent and rescaled from the SFR,


where is the star formation efficiency (Krumholz et al., 2012),


is the free-fall timescale at the mean density of molecular clouds . Finally, the timescale for grain destruction, and grain growth are computed as in de Bennassuti et al. (2014). The latter timescale depends on the gas phase metallicity, temperature and density of molecular clouds,


where we have assumed that grains which experience grain growth have a typical size of µm (Hirashita & Voshchinnikov, 2014). If and , the accretion timescale for gas at solar metallicity is only 2  Myr (Asano et al., 2013).

Below we apply the chemical evolution model to each of the two galaxies under investigation. Throughout the following, we adopt a solar metallicity of (Asplund et al., 2009).

3.1 Sbs 0335052

The observed mass of metals in SBS 0335052  is (the lower limit corresponds to pure atomic gas and the upper one to the total gas mass, see Table 1). The observed dust mass is . Hence, the total mass in heavy elements ranges from to . As described in Sect. 2, the maximum dust mass that can be produced by self-enrichment from observed stellar populations in SBS 0335052  is , times lower than the estimated dust mass reported in Table 1 (Hunt et al., 2014) and lower than the lowest limit on the dust mass reported by Thuan et al. (1999). It is therefore unlikely that the origin of the dust in SBS 0335052 is self-enrichment. In fact, the same stars responsible for metal pre-enrichment may have also formed dust. Alternatively, the dust mass may have formed in situ by means of grain growth. We examine each of these two possibilities in turn.

We first assume that the stars observed in SBS 0335052, with a total mass of , have a mean age of 6 Myr and have formed at a constant rate of /yr with a Salpeter IMF (see the values in Table 1). Under these conditions, only stars with masses had the time to evolve and the total mass of heavy elements and dust injected in the ISM by SNe is and , respectively, much smaller than observed. From eq. (3), we can estimate the mass of metals that was originally present in SBS 0335052, , where . This is equal to the mass presently observed, corrected for astration and self-enrichment,


and we find . Assuming the Salpeter IMF-averaged dust and metal yields for a fully-evolved stellar population with a metallicity ( and ), the maximum mass of dust that SBS 0335052 could have achieved by pre-enrichment can be estimated as


which is only of the observed value.

We can repeat the same calculation but assuming that the observed stars in SBS 0335052  have a mean age of 13.1 Myr, a total stellar mass of and have formed with a constant SFR of /yr with a Salpeter IMF (see the values in parenthesis in Table 1). In this case, newly formed stars with masses produce of heavy elements and of dust, too small to account for the observed dust mass. Using eq. (11), we find that the mass of heavy elements achieved by means of pre-enrichment at is , which corresponds to a maximum dust mass of (from eq. 12), of the observed value.

It is important to stress that the above values of should be regarded as upper mass limits. In fact, if we were to consider only the atomic gas rather than the total (including the putative molecular component), the dust masses allowed by pre-enrichment would be even lower, in both cases. Moreover, eq. (12) is based on the implicit assumption that all the dust produced by previous stellar generations has been conserved in the ISM, without undergoing any destruction by interstellar shocks. Hence, pre-enrichment cannot account for the observed dust masses, even if we were to consider a factor 3-4 reduction in the observed dust mass, either by using more emissive grain mixtures (Jones et al., 2013), or by artificially lowering the observed 870 µm dust flux in the SED (see Sect. 2.4).

Independently of the adopted stellar ages, a major fraction of the existing mass of dust in SBS 0335052 must have formed by means of grain growth in the dense phase of the ISM.

In Figure 4 we show the results of chemical evolution models. Since it is impossible to constrain the initial value of dust mass that SBS 0335052 has inherited from previous stellar generations, we have explored two limiting cases: in the first one, we take the observed gas density of 1500 cm (see Table 1) and we start from the minimum initial dust mass that allows the model to reproduce the observations (red shaded region between the two solid lines). This model shows that if the stellar age is 6 Myr, SBS 0335052 must start with the maximum possible initial dust mass predicted by eq. (12), grain growth accounts for of the existing dust mass, with pre-enrichment providing the remaining . If the stellar age is 13.1 Myr, due to the longer time available for grain growth, SBS 0335052  can start with a dust mass that is of the maximum value achieved by pre-enrichment and grain growth accounts for of the observed dust mass. In the second model (blue shaded region between the two shaded lines), we assume an initial dust mass of only , as if the chemical initial conditions inherited from previous stellar generations were not favourable to dust pre-enrichment. Under this pessimistic scenario, a gas density of () would allow grain growth to increase the dust mass, reaching the observed value in 6 Myr (13.1 Myr). The above results have been obtained solving the system of equations (1) - (4) assuming an initial gas mass (closed-box approximation) and fixing the free parameters and to reproduce the mass of molecular gas component at . For 1500 cm  this constrains the star formation efficiency to be and the fraction of molecular gas to be .

Hence we conclude that, provided that a major fraction of the dense gas in SBS 0335052 is at densities cmcm, the observed dust mass in SBS 0335052  can be reproduced by means of grain growth.

3.2 I Zw 18

We next analyse the evolution of I Zw 18. The observed mass of metals and dust are (the lower limit corresponds to pure atomic gas and the upper one to the total gas mass, see Table 1) and , resulting in a total mass of heavy elements of . Depending on the adopted stellar ages (), between 4 and 60% of the observed metal mass can be achieved by self-enrichment, the remaining fraction must have come from previous stellar generations. The same is true for the dust mass: even assuming that all the dust injected by SNe in the ISM is conserved, self-enrichment can produce between and of the existing dust mass. Using eqs. (11) and (12), the initial mass of heavy elements and dust can be estimated to be:

where the upper (lower) initial values have been obtained assuming a stellar age of 6 (18.3) Myr and considering only atomic versus total gas mass. Because the initial maximum dust masses are a factor 2 – 4 larger than the observed value, all of the existing dust mass in I Zw 18  could originate from dust pre-enrichment.

Figure 5 shows the results of chemical evolution models. Similarly to the case of SBS 0335052, we solve the system of equations (1) - (4) in the closed-box approximation with parameters and fixed to reproduce the mass of molecular gas component at . We first fix the gas density to its observed value,  = 100 cm, and we run the model starting from the minimum initial dust mass that allows the observed dust mass to be reproduced (red shaded region between the two solid lines). This implies a star formation efficiency and a molecular gas fraction of . It is clear that grain growth is negligible and that the required initial dust mass is smaller when the stellar age is 18.3 Myr, due to the larger contribution given by self-enrichment. According to this scenario, the system starts with an initial dust mass of , and then evolves very slowly, with dust injected by newly-formed stars, partly compensated by grain destruction by interstellar shocks and astration. As a result, more than of the observed dust mass is inherited from pre-enrichment, with grain growth making up the rest. This is different from the solid lines shown in Fig. 4, and a consequence of the lower gas density observed in I Zw 18, which causes grain growth to be inefficient. The dashed lines in Fig. 5 show the evolution when – by construction – we impose grain growth to provide the dominant contribution to the final dust mass. In this case, we can start from a negligible initial dust mass but the required gas densities are in the range cm cm, values which are not supported by observations of any of the gas phases.

Figure 4: The predicted evolution of the dust mass in SBS 0335052  is compared with the observed value (grey data point). The upper grey shaded region indicate the range of variation of the inferred stellar ages. The maximum initial dust mass achieved by pre-enrichment is illustrated by the solid red line in the lower grey shaded region. The red region illustrate the range of models where the observed dust mass is reproduced adopting 1500 cm  to compute the grain growth timescale and requiring an initial dust mass from pre-enrichment. The blue region illustrate models where dust pre-enrichment is negligible and we adjust the density of dense gas so that the observed dust mass is reproduced by means of grain growth (the required range of is also shown, see text).
Figure 5: Same as Fig.4 but for I Zw 18.

4 Implications for high-redshift galaxies

The strong dependence of grain growth and the assembly of dust mass on ISM density has profound implications for early galaxy evolution. To date, only one star-forming galaxy at , A1689-zD1 with , has a clear detection of dust emission (Watson et al., 2015). This galaxy has a (lensing-corrected) stellar mass , and SFR yr. With an estimated dust mass of , the dust-to-stellar mass ratio for this galaxy is relatively high, 0.02, comparable to the highest values found for local star-forming galaxies at similar masses (e.g., Skibba et al., 2011). The age of A1689-zD1 is estimated to be 80 Myr, at a redshift when the universe was 500 Myr old.

Despite extensive efforts, dust emission in other star-forming galaxies at comparable redshifts () has not yet been detected (e.g., IOK-1, z8-GND-5296: Ota et al., 2014; Schaerer et al., 2015). Thus, we predict that A1689-zD1 will be found to have a dense ISM, and thus able to assemble a considerable dust mass over the short times available at these redshifts. Our findings suggest that dust mass can be a sensitive indicator of the physical conditions in the ISM, and that metallicity alone is insufficient to determine the amount of dust.

5 Conclusions

In this paper we have investigated the origin of the observed dust masses in the two most metal-poor local dwarf galaxies, SBS 0335052 and I Zw 18. Despite their comparable metallicities, gas and stellar masses, these two galaxies show a huge variation in their dust content, with a dust mass of  in SBS 0335052, as inferred by recent ALMA observations (H14), and a dust mass of only 340  in I Zw 18. By means of a chemical evolution model with dust, we find that:

  • The observed stellar population in SBS 0335052 can not account for the existing metal and dust masses, hence previous stellar populations must have pre-enriched the ISM of the galaxy.

  • Even assuming the maximum possible stellar dust yields, the same stars which have pre-enriched the ISM of SBS 0335052 could have injected a dust mass which is at most 15% of the observed value. Hence, a major fraction of the observed dust mass must originate in situ through grain growth.

  • The observed gas density of SBS 0335052 is large enough to activate efficient grain growth. If  = 1500 cm, grain growth can account for more than 85% of the existing dust mass, with dust pre-enrichment making up the rest.

  • Despite the longer age spread estimated for the stellar population in I Zw 18, only between 4 and 60% of the observed metals are produced by self-enrichment through SN explosions of massive stellar progenitors (). Hence, the metallicity has been mostly inherited by previous stellar generations.

  • Due to the smaller gas density of I Zw 18, grain growth is very inefficient. Since dust injected by newly-formed stars is partly compensated by grain destruction by interstellar shocks and astration, more than of the existing dust mass is inherited from pre-enrichment, with grain growth making up the rest.

Since dust grains can be efficiently destroyed by interstellar shocks, it is very hard to predict the inital mass of dust that can be assembled by pre-enrichment. For this reason, we have also explored a limiting case where the galaxies start with a negligible dust content and achieve all of their dust mass by means of grain growth. This requires the gas density to be larger than inferred from observations:  cm for SBS 0335052 and  cm cm for I Zw 18. While for SBS 0335052  is within the values estimated by Johnson et al. (2009) for the ionized gas densities (see their Table 4), no observations for I Zw 18  suggest similarly high gas densities. However, independently of these considerations, our study suggests that the widely different dust masses in SBS 0335052 and I Zw 18 reflect the different efficiencies of grain growth in their ISM, which – given the comparable metallicity – is likely to originate from the different gas densities of the two galaxies.


We thank Luca Graziani for his insightful comments and Robert Nikutta for a careful analysis of the SED fitting. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 306476. LH is grateful to funding from INAF-PRIN 2012/2015.


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