arXiv subjects

Simon C. O. Glover

Publications and source records attributed to Simon C. O. Glover.

At least 271 records · Page 15Linked to original sources

arXiv2015

Synthetic observations of molecular clouds in a galactic center environment: I. Studying maps of column density and integrated intensity

We run numerical simulations of molecular clouds (MCs), adopting properties similar to those found in the Central Molecular Zone (CMZ) of the Milky Way. For this, we employ the moving mesh code Arepo and perform simulations which account for a simplified treatment of time-dependent chemistry and the non-isothermal nature of gas and dust. We perform simulations using an initial density of n_0 = 10^3 cm^{-3} and a mass of 1.3x10^5 M_sun. Furthermore, we vary the virial parameter, defined as the ratio of kinetic and potential energy, alpha = E_{kin} / |E_{pot}|, by adjusting the velocity dispersion. We set it to alpha = 0.5, 2.0 and 8.0, in order to analyze the impact of the kinetic energy on our results. We account for the extreme conditions in the CMZ and increase both the interstellar radiation field (ISRF) and the cosmic-ray flux (CRF) by a factor of 1000 compared to the values found in the solar neighbourhood. We use the radiative transfer code RADMC-3D to compute synthetic images in various diagnostic lines. These are [CII] at 158 micron, [OI] (145 micron), [OI] (63 micron), 12CO (J = 1 -> 0) and 13CO (J = 1 -> 0) at 2600 micron and 2720 micron, respectively. When alpha is large, the turbulence disperses much of the gas in the cloud, reducing its mean density and allowing the ISRF to penetrate more deeply into the cloud's interior. This significantly alters the chemical composition of the cloud, leading to the dissociation of a significant amount of the molecular gas. On the other hand, when alpha is small, the cloud remains compact, allowing more of the molecular gas to survive. We show that in each case the atomic tracers accurately reflect most of the physical properties of both the H2 and the total gas of the cloud and that they provide a useful alternative to molecular lines when studying the ISM in the CMZ.

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arXiv2015

Impact of supernova and cosmic-ray driving on the surface brightness of the galactic halo in soft X-rays

The halo of the Milky Way contains a hot plasma with a surface brightness in soft X-rays of the order $10^{-12}$erg cm$^{-2}$ s$^{-1}$ deg$^{-2}$. The origin of this gas is unclear, but so far numerical models of galactic star formation have failed to reproduce such a large surface brightness by several orders of magnitude. In this paper, we analyze simulations of the turbulent, magnetized, multi-phase interstellar medium including thermal feedback by supernova explosions as well as cosmic-ray feedback. We include a time-dependent chemical network, self-shielding by gas and dust, and self-gravity. Pure thermal feedback alone is sufficient to produce the observed surface brightness, although it is very sensitive to the supernova rate. Cosmic rays suppress this sensitivity and reduce the surface brightness because they drive cooler outflows. Self-gravity has by far the largest effect because it accumulates the diffuse gas in the disk in dense clumps and filaments, so that supernovae exploding in voids can eject a large amount of hot gas into the halo. This can boost the surface brightness by several orders of magnitude. Although our simulations do not reach a steady state, all simulations produce surface brightness values of the same order of magnitude as the observations, with the exact value depending sensitively on the simulation parameters. We conclude that star formation feedback alone is sufficient to explain the origin of the hot halo gas, but measurements of the surface brightness alone do not provide useful diagnostics for the study of galactic star formation.

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arXiv2015

Lyman-Werner UV Escape Fractions from Primordial Halos

Population III stars can regulate star formation in the primordial Universe in several ways. They can ionize nearby halos, and even if their ionizing photons are trapped by their own halos, their Lyman-Werner (LW) photons can still escape and destroy H$_2$ in other halos, preventing them from cooling and forming stars. LW escape fractions are thus a key parameter in cosmological simulations of early reionization and star formation but have not yet been parametrized for realistic halos by halo or stellar mass. To do so, we perform radiation hydrodynamical simulations of LW UV escape from 9--120 M$_{\odot}$ Pop III stars in $10^5$ to $10^7$ M$_{\odot}$ halos with ZEUS-MP. We find that photons in the LW lines (i.e. those responsible for destroying H$_{2}$ in nearby systems) have escape fractions ranging from 0% to 85%. No LW photons escape the most massive halo in our sample, even from the most massive star. Escape fractions for photons elsewhere in the 11.18--13.6~eV energy range, which can be redshifted into the LW lines at cosmological distances, are generally much higher, being above 60% for all but the least massive stars in the most massive halos. We find that shielding of H$_2$ by neutral hydrogen, which has been neglected in most studies to date, produces escape fractions that are up to a factor of three smaller than those predicted by H$_2$ self-shielding alone.

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arXiv2015

On the nature of star-forming filaments: II. Sub-filaments and velocities

We show that hydrodynamic turbulent cloud simulations naturally produce large filaments made up of a network of smaller and coherent sub-filaments. Such simulations resemble observations of filaments and fibres in nearby molecular clouds. The sub-filaments are dynamical features formed at the stagnation points of the turbulent velocity field where shocks dissipate the turbulent energy. They are a ubiquitous feature of the simulated clouds, which appear from the beginning of the simulation and are not formed by gradual fragmentation of larger filaments. Most of the sub-filaments are gravitationally sub-critical and do not fragment into cores, however, there is also a significant fraction of supercritical sub-filaments which break up into star-forming cores. The sub-filaments are coherent along their length, and the residual velocities along their spine show that they are subsonically contracting without any ordered rotation on scales of ~0.1 pc. Accretion flows along the sub-filaments can feed material into star forming cores embedded within the network. The overall mass in sub-filaments and the number of sub-filaments increases as the cloud evolves. We propose that the formation of filaments and sub-filaments is a natural consequence of the turbulent cascade in the complex multi-phase interstellar medium. Sub-filaments are formed by the high wavenumber, small scale modes in the turbulent velocity field. These are then stretched by local shear motions and gathered together by a combination of low wavenumber modes and gravitational contraction on larger scales, and by doing so build up the extended filaments observed in column density maps.

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arXiv2015

Simulating the formation of massive seed black holes in the early Universe. II: Impact of rate coefficient uncertainties

We investigate how uncertainties in the chemical and cooling rate coefficients relevant for a metal-free gas influence our ability to determine the critical ultraviolet field strength required to suppress H2 cooling in high-redshift atomic cooling halos. The suppression of H2 cooling is a necessary prerequisite for the gas to undergo direct collapse and form an intermediate mass black hole. These black holes can then act as seeds for the growth of the supermassive black holes (SMBHs) observed at redshifts $z \sim 6$. The viability of this model for SMBH formation depends on the critical ultraviolet field strength, Jcrit: if this is too large, then too few seeds will form to explain the observed number density of SMBHs. We show in this paper that there are five key chemical reactions whose rate coefficients are uncertain enough to significantly affect Jcrit. The most important of these is the collisional ionization of hydrogen by collisions with other hydrogen atoms, as the rate for this process is very poorly constrained at the low energies relevant for direct collapse. The total uncertainty introduced into Jcrit by this and the other four reactions could in the worst case approach a factor of five. We also show that the use of outdated or inappropriate values for the rates of some chemical reactions in previous studies of the direct collapse mechanism may have significantly affected the values of Jcrit determined by these studies.

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arXiv2015

How an improved implementation of H2 self-shielding influences the formation of massive stars and black holes

High redshift quasars at z>6 have masses up to ~$10^9$ M$_\odot$. One of the pathways to their formation includes direct collapse of gas, forming a supermassive star, precursor of the black hole seed. The conditions for direct collapse are more easily achievable in metal-free haloes, where atomic hydrogen cooling operates and molecular hydrogen (H2) formation is inhibited by a strong external UV flux. Above a certain value of UV flux (J_crit), the gas in a halo collapses isothermally at ~$10^4$ K and provides the conditions for supermassive star formation. However, H2 can self-shield, reducing the effect of photodissociation. So far, most numerical studies used the local Jeans length to calculate the column densities for self-shielding. We implement an improved method for the determination of column densities in 3D simulations and analyse its effect on the value of J_crit. This new method captures the gas geometry and velocity field and enables us to properly determine the direction-dependent self-shielding factor of H2 against photodissociating radiation. We find a value of J_crit that is a factor of two smaller than with the Jeans approach (~2000 J_21 vs. ~4000 J_21). The main reason for this difference is the strong directional dependence of the H2 column density. With this lower value of J_crit, the number of haloes exposed to a flux >J_crit is larger by more than an order of magnitude compared to previous studies. This may translate into a similar enhancement in the predicted number density of black hole seeds.

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arXiv2015

Does the CO-to-H2 conversion factor depend on the star formation rate?

We present a series of numerical simulations that explore how the `X-factor', $X_{CO}$ -- the conversion factor between the observed integrated CO emission and the column density of molecular hydrogen -- varies with the environmental conditions in which a molecular cloud is placed. Our investigation is centred around two environmental conditions in particular: the cosmic ray ionisation rate (CRIR) and the strength of the interstellar radiation field (ISRF). Since both these properties of the interstellar medium have their origins in massive stars, we make the assumption in this paper that both the strength of the ISRF and the CRIR scale linearly with the local star formation rate (SFR). The cloud modelling in this study first involves running numerical simulations that capture the cloud dynamics, as well as the time-dependent chemistry, and ISM heating and cooling. These simulations are then post-processed with a line radiative transfer code to create synthetic 12CO (1-0) emission maps from which $X_{CO}$ can be calculated. We find that for 1e4 solar mass virialised clouds with mean density 100 cm$^{-3}$, $X_{CO}$ is only weakly dependent on the local SFR, varying by a factor of a few over two orders of magnitude in SFR. In contrast, we find that for similar clouds but with masses of 1e5 solar masses, the X-factor will vary by an order of magnitude over the same range in SFR, implying that extra-galactic star formation laws should be viewed with caution. However, for denser ($10^4$ cm$^{-3}$), super-virial clouds such as those found at the centre of the Milky Way, the X-factor is once again independent of the local SFR.

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arXiv2015

Star formation efficiencies of molecular clouds in a galactic center environment

We use the Arepo moving mesh code to simulate the evolution of molecular clouds exposed to a harsh environment similar to that found in the galactic center (GC), in an effort to understand why the star formation efficiency (SFE) of clouds in this environment is so small. Our simulations include a simplified treatment of time-dependent chemistry and account for the highly non-isothermal nature of the gas and the dust. We model clouds with a total mass of 1.3x10^5 M_{sun} and explore the effects of varying the mean cloud density and the virial parameter, alpha = E_{kin}/|E_{pot}|. We vary the latter from alpha = 0.5 to alpha = 8.0, and so many of the clouds that we simulate are gravitationally unbound. We expose our model clouds to an interstellar radiation field (ISRF) and cosmic ray flux (CRF) that are both a factor of 1000 higher than the values found in the solar neighbourhood. As a reference, we also run simulations with local solar neighbourhood values of the ISRF and the CRF in order to better constrain the effects of the extreme conditions in the GC on the SFE. Despite the harsh environment and the large turbulent velocity dispersions adopted, we find that all of the simulated clouds form stars within less than a gravitational free-fall time. Increasing the virial parameter from alpha = 0.5 to alpha = 8.0 decreases the SFE by a factor ~4-10, while increasing the ISRF/CRF by a factor of 1000 decreases the SFE again by a factor ~2-6. However, even in our most unbound clouds, the SFE remains higher than that inferred for real GC clouds. We therefore conclude that high levels of turbulence and strong external heating are not enough by themselves to lead to a persistently low SFE at the center of the Galaxy.

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arXiv2015

Structure analysis of simulated molecular clouds with the Delta-variance

We employ the Delta-variance analysis and study the turbulent gas dynamics of simulated molecular clouds (MCs). Our models account for a simplified treatment of time-dependent chemistry and the non-isothermal nature of the gas. We investigate simulations using three different initial mean number densities of n_0 = 30, 100 and 300 cm^{-3} that span the range of values typical for MCs in the solar neighbourhood. Furthermore, we model the CO line emission in a post-processing step using a radiative transfer code. We evaluate Delta-variance spectra for centroid velocity (CV) maps as well as for integrated intensity and column density maps for various chemical components: the total, H2 and 12CO number density and the integrated intensity of both the 12CO and 13CO (J = 1 -> 0) lines. The spectral slopes of the Delta-variance computed on the CV maps for the total and H2 number density are significantly steeper compared to the different CO tracers. We find slopes for the linewidth-size relation ranging from 0.4 to 0.7 for the total and H2 density models, while the slopes for the various CO tracers range from 0.2 to 0.4 and underestimate the values for the total and H2 density by a factor of 1.5-3.0. We demonstrate that optical depth effects can significantly alter the Delta-variance spectra. Furthermore, we report a critical density threshold of ~100 cm^{-3} at which the Delta-variance slopes of the various CO tracers change sign. We thus conclude that carbon monoxide traces the total cloud structure well only if the average cloud density lies above this limit.

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arXiv2015

Constraining the primordial initial mass function with stellar archaeology

We present a new near-field cosmological probe of the initial mass function (IMF) of the first stars. Specifically, we constrain the lower-mass limit of the Population III (Pop III) IMF with the total number of stars in large, unbiased surveys of the Milky Way. We model the early star formation history in a Milky Way-like halo with a semi-analytic approach, based on Monte-Carlo sampling of dark matter merger trees, combined with a treatment of the most important feedback mechanisms. Assuming a logarithmically flat Pop III IMF and varying its low mass limit, we derive the number of expected survivors of these first stars, using them to estimate the probability to detect any such Pop III fossil in stellar archaeological surveys. Following our analysis, the most promising region to find possible Pop III survivors is the stellar halo of the Milky Way, which is the best target for future surveys. We find that if no genuine Pop III survivor is detected in a sample size of $4 \times 10^6$ ($2 \times 10^7$) halo stars with well-controlled selection effects, then we can exclude the hypothesis that the primordial IMF extended down below $0.8 M_\odot$ at a confidence level of 68% (99%). With the sample size of the Hamburg/ESO survey, we can tentatively exclude Pop III stars with masses below $0.65 M_\odot$ with a confidence level of 95%, although this is subject to significant uncertainties. To fully harness the potential of our approach, future large surveys are needed that employ uniform, unbiased selection strategies for high-resolution spectroscopic follow-up.

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arXiv2015

Modelling [CI] emission from turbulent molecular clouds

We use detailed numerical simulations of the coupled chemical, thermal and dynamical evolution of the gas in a turbulent molecular cloud to study the usefulness of the [CI] 609 micron and 370 micron fine structure emission lines as tracers of cloud structure. Emission from these lines is observed throughout molecular clouds, and yet the question of what we can learn from them about the physics of the clouds remains largely unexplored. We show that the fact that [CI] emission is widespread within molecular clouds is a simple consequence of the fact that the clouds are dominated by turbulent motions. Turbulence creates large density inhomogeneities, allowing radiation to penetrate deeply into the clouds. As a result, [CI] emitting gas is found throughout the cloud, rather than being concentrated at the edges. We examine how well we can use [CI] emission to trace the structure of the cloud, and show that the integrated intensity of the 609 micron line traces column density accurately over a wide range of visual extinctions. For extinctions greater than a few, [CI] and 13CO both perform well, but [CI] becomes a superior tracer of column densities for visual extinctions A_V <= 3 We have also studied the distribution of [CI] excitation temperatures in the gas, and show that these are typically smaller than the kinetic temperature, indicating that most of the carbon atoms are not in local thermodynamic equilibrium. We discuss how best to determine T_ex from observations of the [CI] lines, and how to use these values to estimate the column density of neutral atomic carbon. We show that even in the best case, we tend to systematically underestimate the atomic carbon content of the gas. Our results suggest that observationally-derived estimates of the atomic carbon content of real GMCs could be in error by as much as a factor of two.

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arXiv2014

Physical Processes in the Interstellar Medium

Interstellar space is filled with a dilute mixture of charged particles, atoms, molecules and dust grains, called the interstellar medium (ISM). Understanding its physical properties and dynamical behavior is of pivotal importance to many areas of astronomy and astrophysics. Galaxy formation and evolution, the formation of stars, cosmic nucleosynthesis, the origin of large complex, prebiotic molecules and the abundance, structure and growth of dust grains which constitute the fundamental building blocks of planets, all these processes are intimately coupled to the physics of the interstellar medium. However, despite its importance, its structure and evolution is still not fully understood. Observations reveal that the interstellar medium is highly turbulent, consists of different chemical phases, and is characterized by complex structure on all resolvable spatial and temporal scales. Our current numerical and theoretical models describe it as a strongly coupled system that is far from equilibrium and where the different components are intricately linked together by complex feedback loops. Describing the interstellar medium is truly a multi-scale and multi-physics problem. In these lecture notes we introduce the microphysics necessary to better understand the interstellar medium. We review the relations between large-scale and small-scale dynamics, we consider turbulence as one of the key drivers of galactic evolution, and we review the physical processes that lead to the formation of dense molecular clouds and that govern stellar birth in their interior.

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arXiv2014

A new approach to determine optically thick H2 cooling and its effect on primordial star formation

We present a new method for estimating the H2 cooling rate in the optically thick regime in simulations of primordial star formation. Our new approach is based on the TreeCol algorithm, which projects matter distributions onto a spherical grid to create maps of column densities for each fluid element in the computational domain. We have improved this algorithm by using the relative gas velocities, to weight the individual matter contributions with the relative spectral line overlaps, in order to properly account for the Doppler effect. We compare our new method to the widely used Sobolev approximation, which yields an estimate for the column density based on the local velocity gradient and the thermal velocity. This approach generally underestimates the photon escape probability, because it neglects the density gradient and the actual shape of the cloud. We present a correction factor for the true line overlap in the Sobolev approximation and a new method based on local quantities, which fits the exact results reasonably well during the collapse of the cloud, with the error in the cooling rates always being less than 10%. Analytical fitting formulae fail at determining the photon escape probability after formation of the first protostar (error of 40%) because they are based on the assumption of spherical symmetry and therefore break down once a protostellar accretion disc has formed. Our method yields lower temperatures and hence promotes fragmentation for densities above 10^{10}/ccm at a distance of 200AU from the first protostar. Since the overall accretion rates are hardly affected by the cooling implementation, we expect Pop III stars to have lower masses in our simulations, compared to the results of previous simulations that used the Sobolev approximation.

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arXiv2014

Dust and Gas in the Magellanic Clouds from the HERITAGE Herschel Key Project. II. Gas-to-Dust Ratio Variations across ISM Phases

The spatial variations of the gas-to-dust ratio (GDR) provide constraints on the chemical evolution and lifecycle of dust in galaxies. We examine the relation between dust and gas at 10-50 pc resolution in the Large and Small Magellanic Clouds (LMC and SMC) based on Herschel far-infrared (FIR), H I 21 cm, CO, and Halpha observations. In the diffuse atomic ISM, we derive the gas-to-dust ratio as the slope of the dust-gas relation and find gas-to-dust ratios of 380+250-130 in the LMC, and 1200+1600-420 in the SMC, not including helium. The atomic-to-molecular transition is located at dust surface densities of 0.05 Mo pc-2 in the LMC and 0.03 Mo pc-2 in the SMC, corresponding to AV ~ 0.4 and 0.2, respectively. We investigate the range of CO-to-H2 conversion factor to best account for all the molecular gas in the beam of the observations, and find upper limits on XCO to be 6x1020 cm-2 K-1 km-1 s in the LMC (Z=0.5Zo) at 15 pc resolution, and 4x 1021 cm-2 K-1 km-1 s in the SMC (Z=0.2Zo) at 45 pc resolution. In the LMC, the slope of the dust-gas relation in the dense ISM is lower than in the diffuse ISM by a factor ~2, even after accounting for the effects of CO-dark H2 in the translucent envelopes of molecular clouds. Coagulation of dust grains and the subsequent dust emissivity increase in molecular clouds, and/or accretion of gas-phase metals onto dust grains, and the subsequent dust abundance (dust-to-gas ratio) increase in molecular clouds could explain the observations. In the SMC, variations in the dust-gas slope caused by coagulation or accretion are degenerate with the effects of CO-dark H2. Within the expected 5--20 times Galactic XCO range, the dust-gas slope can be either constant or decrease by a factor of several across ISM phases. Further modeling and observations are required to break the degeneracy between dust grain coagulation, accretion, and CO-dark H2.

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arXiv2014

Centroid Velocity Statistics of Molecular Clouds

We compute structure functions and Fourier spectra of 2D centroid velocity (CV) maps in order to study the gas dynamics of typical molecular clouds (MCs) in numerical simulations. We account for a simplified treatment of time-dependent chemistry and the non-isothermal nature of the gas and use a 3D radiative transfer tool to model the CO line emission in a post-processing step. We perform simulations using three different initial mean number densities of n_0 = 30, 100 and 300 cm^{-3} to span a range of typical values for dense gas clouds in the solar neighbourhood. We compute slopes of the centroid velocity increment structure functions (CVISF) and of Fourier spectra for different chemical components: the total density, H2 number density, 12CO number density as well as the integrated intensity of 12CO (J=1-0) and 13CO (J=1-0). We show that optical depth effects can significantly affect the slopes derived for the CVISF, which also leads to different scaling properties for the Fourier spectra. The slopes of CVISF and Fourier spectra for H2 are significantly steeper than those for the different CO tracers, independent of the density and the numerical resolution. This is due to the larger space-filling factor of H2 as it is better able to self-shield in diffuse regions, leading to a larger fractal co-dimension compared to CO.

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arXiv2014

The $^{12}$CO/$^{13}$CO ratio in turbulent molecular clouds

The $^{13}$CO molecule is often used as a column density tracer in regions where the $^{12}$CO emission saturates. The $^{13}$CO column density is then related to that of $^{12}$CO by a uniform isotopic ratio. A similar approximation is frequently used when deriving $^{13}$CO emission maps from numerical simulations of molecular clouds. To test this assumption we calculate the $^{12}$CO/$^{13}$CO ratio self-consistently, taking the isotope selective photodissociation and the chemical fractionation of CO into account. We model the coupled chemical, thermal and dynamical evolution and the emergent $^{13}$CO emission of isolated, starless molecular clouds in various environments. Selective photodissociation has a minimal effect on the ratio, while the chemical fractionation causes a factor of 2-3 decrease at intermediate cloud depths. The variation correlates with both the $^{12}$CO and the $^{13}$CO column densities. Neglecting the depth dependence results in $\leq$60 per cent error in $^{12}$CO column densities derived from $^{13}$CO. The same assumption causes $\leq$50 per cent disparity in the $^{13}$CO emission derived from simulated clouds. We show that the discrepancies can be corrected by a fitting formula. The formula is consistent with millimetre-wavelength isotopic ratio measurements of dense molecular clouds, but underestimates the ratios from the ultraviolet absorption of diffuse regions.

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arXiv2014

On the nature of star-forming filaments: I. Filament morphologies

We use a suite of high resolution molecular cloud simulations carried out with the moving mesh code Arepo to explore the nature of star-forming filaments. The simulated filaments are identified and categorised from column density maps in the same manner as for recent Herschel observations. When fit with a Plummer-like profile the filaments are in excellent agreement with observations, and have shallow power-law profiles of p~2.2 without the need for magnetic support. When data within 1 pc of the filament centre is fitted with a Gaussian function, the average FWHM is ~0.3 pc, in agreement with predictions for accreting filaments. However, if the fit is constructed using only the inner regions, as in Herschel observations, the resulting FWHM is only ~0.2 pc. This value is larger than that measured in IC 5146 and Taurus, but is similar to that found in the Planck Galactic Cold Cores and in Cygnus X. The simulated filaments have a range of widths rather than a constant value. When the column density maps are compared to the 3D gas densities, the filaments seen in column density do not belong to a single structure. Instead, they are made up of a network of short ribbon-like sub-filaments reminiscent of those seen in Taurus. The sub-filaments are pre-existing within the simulated clouds, have radii similar to their Jeans radius, and are not primarily formed through fragmentation of the larger filament seen in column density. Instead, small filamentary clumps are swept together into a single column density structure by the large-scale collapse of the cloud.

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arXiv2014

On column density thresholds and the star formation rate

We present the results of a numerical study designed to address the question of whether there is a column density threshold for star formation within molecular clouds. We have simulated a large number of different clouds, with volume and column densities spanning a wide range of different values, using a state-of-the-art model for the coupled chemical, thermal and dynamical evolution of the gas. We show that star formation is only possible in regions where the mean (area-averaged) column density exceeds $10^{21} \: {\rm cm^{-2}}$. Within the clouds, we also show that there is a good correlation between the mass of gas above a K-band extinction $A_{\rm K} = 0.8$ and the star formation rate (SFR), in agreement with recent observational work. Previously, this relationship has been explained in terms of a correlation between the SFR and the mass in dense gas. However, we find that this correlation is weaker and more time-dependent than that between the SFR and the column density. In support of previous studies, we argue that dust shielding is the key process: the true correlation is one between the SFR and the mass in cold, well-shielded gas, and the latter correlates better with the column density than the volume density.

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