Tracer Of Column Density Research Articles

Modelling the dust emission of a filament in the Taurus molecular cloud

Context. Dust emission is an important tool in studies of star-forming clouds as a tracer of column density. This is done indirectly via the dust evolution that is connected to the history and physical conditions of the clouds. Aims. We examine the radiative transfer (RT) modelling of dust emission over an extended cloud region, using a filament in the Taurus molecular cloud as an example. We examine how well far-infrared (FIR) observations can be used to determine both the cloud and the dust properties. Methods. Using different assumptions on the cloud shape, radiation field, and dust properties, we fit RT models to Herschel observations of the Taurus filament. We made further comparisons with measurements of the near-infrared extinction. The models were used to examine the degeneracies between the different cloud parameters and the dust properties. Results. The results show a significant dependence on the assumed cloud structure and the spectral shape of the external radiation field. If these are constrained to the most likely values, the observations can be explained only if the dust FIR opacity has increased by a factor of 2–3 relative to the values in diffuse medium. However, a narrow range of FIR wavelengths provides only weak evidence of the spatial variations in dust, even in the models covering several square degrees of a molecular cloud. Conclusions. The analysis of FIR dust emission is affected by several sources of uncertainty. Further constraints are therefore needed from observations at shorter wavelengths, especially with respect to trends in dust evolution.

PHANGS–JWST First Results: Mid-infrared Emission Traces Both Gas Column Density and Heating at 100 pc Scales

We compare mid-infrared (mid-IR), extinction-corrected Hα, and CO (2–1) emission at 70–160 pc resolution in the first four PHANGS–JWST targets. We report correlation strengths, intensity ratios, and power-law fits relating emission in JWST’s F770W, F1000W, F1130W, and F2100W bands to CO and Hα. At these scales, CO and Hα each correlate strongly with mid-IR emission, and these correlations are each stronger than the one relating CO to Hα emission. This reflects that mid-IR emission simultaneously acts as a dust column density tracer, leading to a good match with the molecular-gas-tracing CO, and as a heating tracer, leading to a good match with the Hα. By combining mid-IR, CO, and Hα at scales where the overall correlation between cold gas and star formation begins to break down, we are able to separate these two effects. We model the mid-IR above I ν = 0.5 MJy sr−1 at F770W, a cut designed to select regions where the molecular gas dominates the interstellar medium (ISM) mass. This bright emission can be described to first order by a model that combines a CO-tracing component and an Hα-tracing component. The best-fitting models imply that ∼50% of the mid-IR flux arises from molecular gas heated by the diffuse interstellar radiation field, with the remaining ∼50% associated with bright, dusty star-forming regions. We discuss differences between the F770W, F1000W, and F1130W bands and the continuum-dominated F2100W band and suggest next steps for using the mid-IR as an ISM tracer.

Systematic Investigation of Dust and Gaseous CO in 12 Nearby Molecular Clouds

We report on the first uniform and systematic study of dust and molecular gas in nearby molecular clouds. We use surveys of dust extinction and emission to determine the opacity and map the distribution of the dust within a dozen local clouds in order to derive a uniform set of basic cloud properties. We find (1) the average dust opacity 〈κ d,353〉 = 0.8 cm2 g−1 with variations of a factor of ∼2 between clouds, (2) cloud probability density functions are exquisitely described by steeply falling power laws with a narrow range of slope, and (3) a tight scaling relation for the cloud sample, indicative of a cloud population with an exactingly constant average surface density above a common fixed boundary. We compare these results to uniformly analyzed CO surveys. We measure the CO mass conversion factors and assess the efficacy of CO for tracing the physical properties of molecular clouds. We find 〈α CO〉 = 4.31 ± 0.67 M ⊙ (K km s−1 pc2)−1 (corresponding to X CO = 1.97 ×1020 cm−2(K km s−1)−1). We demonstrate that CO observations are a poor tracer of column density and structure on sub-cloud spatial scales. On cloud scales, CO observations can provide measurements consistent with those of the dust, provided data are analyzed in a similar, self-consistent fashion. Measurements of average giant molecular cloud surface density are sensitive to choice of cloud boundary. Care must be exercised to adopt common fixed boundaries when comparing surface densities for cloud populations within and between galaxies.

Resolved observations at 31 GHz of spinning dust emissivity variations in ρ Oph

ABSTRACT The ρ Oph molecular cloud is one of the best examples of spinning dust emission, first detected by the cosmic background imager (CBI). Here, we present 4.5 arcmin observations with CBI 2 that confirm 31 GHz emission from ρ Oph W, the PDR exposed to B-type star HD 147889, and highlight the absence of signal from S1, the brightest IR nebula in the complex. In order to quantify an association with dust-related emission mechanisms, we calculated correlations at different angular resolutions between the 31 GHz map and proxies for the column density of IR emitters, dust radiance, and optical depth templates. We found that the 31 GHz emission correlates best with the PAH column density tracers, while the correlation with the dust radiance improves when considering emission that is more extended (from the shorter baselines), suggesting that the angular resolution of the observations affects the correlation results. A proxy for the spinning dust emissivity reveals large variations within the complex, with a dynamic range of 25 at 3σ and a variation by a factor of at least 23, at 3σ, between the peak in ρ Oph W and the location of S1, which means that environmental factors are responsible for boosting spinning dust emissivities locally.

CALIBRATING COLUMN DENSITY TRACERS WITH GAMMA-RAY OBSERVATIONS OF THE ρ OPHIUCHI MOLECULAR CLOUD

ABSTRACT Diffuse gamma-ray emission from interstellar clouds results largely from cosmic ray (CR) proton collisions with ambient gas, regardless of the gas state, temperature, or dust properties of the cloud. The interstellar medium is predominantly transparent to both CRs and gamma-rays, so GeV emission is a unique probe of the total gas column density. The gamma-ray emissivity of a cloud of known column density is then a measure of the impinging CR population and may be used to map the k-scale CR distribution in the Galaxy. To this end, we test a number of commonly used column density tracers to evaluate their effectiveness in modeling the GeV emission from the relatively quiescent, nearby ρ Ophiuchi molecular cloud. We confirm that both H i and an appropriate tracer are required to reproduce the total gas column densities probed by diffuse gamma-ray emisison. We find that the optical depth at 353 GHz ( ) from Planck best reproduces the gamma-ray data overall, based on the test statistic across the entire region of interest, but near-infrared stellar extinction also performs very well, with smaller spatial residuals in the densest parts of the cloud.

CH AS A MOLECULAR GAS TRACER AND C-SHOCK TRACER ACROSS A MOLECULAR CLOUD BOUNDARY IN TAURUS

ABSTRACT We present new observations of all three ground-state transitions of the methylidyne (CH) radical and all four ground-state transitions of the hydroxyl (OH) radical toward a sharp boundary region of the Taurus molecular cloud. These data were analyzed in conjunction with existing CO and dust images. The derived CH abundance is consistent with previous observations of translucent clouds (0.8 ≤ A v ≤ 2.1 mag). The X(CH)-factor is nearly a constant (1.0 ± 0.06) × 1022 cm−2 K−1 km−1 s in this extinction range, with less dispersion than that of the more widely used molecular tracers CO and OH. CH turns out be a better tracer of total column density in such an intermediate extinction range than CO or OH. Compared with previous observations, CH is overabundant below 1 mag extinction. Such an overabundance of CH is consistent with the presence of a C-shock. CH has two kinematic components, one of which shifts from 5.3 to 6 km s−1, while the other stays at 6.8 km s−1 when moving from outside toward inside of the cloud. These velocity behaviors exactly match previous OH observation. The shifting of the two kinematic components indicates colliding streams or gas flow at the boundary region, which could be the cause of the C-shock.

Three-dimensional distribution of hydrogen fluoride gas toward NGC 6334 I and I(N)

Aims. We investigate the spatial distribution of a collection of absorbing gas clouds, some associated with the dense, massive star-forming core NGC6334 I, and others with diffuse foreground clouds. For the former category, we aim to study the dynamical properties of the clouds in order to assess their potential to feed the accreting protostellar cores. Methods. We use spectral imaging from the Herschel SPIRE iFTS to construct a map of HF absorption at 243 micron in a 6x3.5 arcmin region surrounding NGC6334 I and I(N). Results. The combination of new, spatially fully sampled, but spectrally unresolved mapping with a previous, single-pointing, spectrally resolved HF signature yields a 3D picture of absorbing gas clouds in the direction of NGC6334. Toward core I, the HF equivalent width matches that of the spectrally resolved observation. The distribution of HF absorption is consistent with three of the seven components being associated with this dense star-forming envelope. For two of the remaining four components, our data suggest that these clouds are spatially associated with the larger scale filamentary star-forming complex. Our data also implies a lack of gas phase HF in the envelope of core I(N). Using a simple description of adsorption onto and desorption from dust grain surfaces, we show that the overall lower temperature of the envelope of source I(N) is consistent with freeze-out of HF, while it remains in the gas phase in source I. Conclusions. We use the HF molecule as a tracer of column density in diffuse gas (n(H) ~ 10^2 - 10^3 cm^-3), and find that it may uniquely trace a relatively low density portion of the gas reservoir available for star formation that otherwise escapes detection. At higher densities prevailing in protostellar envelopes (>10^4 cm^-3), we find evidence of HF depletion from the gas phase under sufficiently cold conditions.

The James Clerk Maxwell telescope Legacy Survey of the Gould Belt: a molecular line study of the Ophiuchus molecular cloud

CO, $^{13}$CO and C$^{18}$O ${\it J}$ = 3--2 observations are presented of the Ophiuchus molecular cloud. The $^{13}$CO and C$^{18}$O emission is dominated by the Oph A clump, and the Oph B1, B2, C, E, F and J regions. The optically thin(ner) C$^{18}$O line is used as a column density tracer, from which the gravitational binding energy is estimated to be $4.5 \times 10^{39}$ J (2282 $M_\odot$ km$^2$ s$^{-2}$). The turbulent kinetic energy is $6.3 \times 10^{38}$ J (320 $M_\odot$ km$^2$ s$^{-2}$), or 7 times less than this, and therefore the Oph cloud as a whole is gravitationally bound. Thirty protostars were searched for high velocity gas, with eight showing outflows, and twenty more having evidence of high velocity gas along their lines-of-sight. The total outflow kinetic energy is $1.3 \times 10^{38}$ J (67 $M_\odot$ km$^2$ s$^{-2}$), corresponding to 21$\%$ of the cloud's turbulent kinetic energy. Although turbulent injection by outflows is significant, but does ${\it not}$ appear to be the dominant source of turbulence in the cloud. 105 dense molecular clumplets were identified, which had radii $\sim$ 0.01--0.05 pc, virial masses $\sim$ 0.1--12 $M_\odot$, luminosities $\sim$ 0.001--0.1 K~km s$^{-1}$ pc$^{-2}$, and excitation temperatures $\sim$ 10--50K. These are consistent with the standard GMC based size-line width relationships, showing that the scaling laws extend down to size scales of hundredths of a parsec, and to sub solar-mass condensations. There is however no compelling evidence that the majority of clumplets are undergoing free-fall collapse, nor that they are pressure confined.

The 12CO/13CO 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.

EVIDENCE OF CONTRIBUTION OF INTERVENING CLOUDS TO GAMMA-RAY BURST'S X-RAY COLUMN DENSITY

The origin of excess of X-ray column density with respect to optical extinction in Gamma-ray bursts (GRBs) is still a puzzle. A proposed explanation of the excess is the photoelectric absorption due to the intervening clouds along a GRB's line-of-sight. We here test this scenario by using the intervening \ion{Mg}{2} absorption as a tracer of the neutral hydrogen column density of the intervening clouds. We identify a connection between large X-ray column density (and large column density ratio of $\mathrm{\log(N_{H,X}/N_{HI})}\sim0.5$) and large neutral hydrogen column density probed by the \ion{Mg}{2} doublet ratio (DR). In addition, GRBs with large X-ray column density (and large ratio of $\mathrm{\log(N_{H,X}/N_{HI})}>0$) tend to have multiple saturated intervening absorbers with $\mathrm{DR<1.2}$. These results therefore indicate an additional contribution of the intervening system to the observed X-ray column density in some GRBs, although the contribution of the host galaxy alone cannot be excluded based on this study.

Mapping of interstellar clouds with infrared light scattered from dust: TMC-1N

Mapping of near-infrared (NIR) scattered light is a recent method for the study of interstellar clouds, complementing other, more commonly used methods, like dust emission and extinction. Our goal is to study the usability of this method on larger scale, and compare the properties of a filament using NIR scattering and other methods. We also study the radiation field and differences in grain emissivity between diffuse and dense areas. We have used scattered J, H, and K band surface brightness WFCAM-observations to map filament TMC-1N in Taurus, covering an area of 1dx1d corresponding to ~(2.44 pc)^2. We have converted the data into optical depth and compared the results with NIR extinction and Herschel observations of submm dust emission. We see the filament in scattered light in all three NIR bands. We note that our WFCAM observations in TMC-1N show notably lower intensity than previous results in Corona Australis using the same method. We show that 3D radiative transfer simulations predict similar scattered surface brightness levels as seen in the observations. However, changing the assumptions about the background can change the results of simulations notably. We derive emissivity by using optical depth in the J band as an independent tracer of column density. We obtain opacity sigma(250um) values 1.7-2.4x10^-25 cm^2/H, depending on assumptions of the extinction curve, which can change the results by over 40%. These values are twice as high as obtained for diffuse areas, at the lower limit of earlier results for denser areas. We show that NIR scattering can be a valuable tool in making high resolution maps. We conclude, however, that NIR scattering observations can be complicated, as the data can show relatively low-level artefacts. This suggests caution when planning and interpreting the observations.

THE COLUMN DENSITY VARIANCE-${\cal M}_s$ RELATIONSHIP

Although there are a wealth of column density tracers for both the molecular and diffuse interstellar medium, there are very few observational studies investigating the relationship between the density variance ($\sigma^2$) and the sonic Mach number (${\cal M}_s$). This is in part due to the fact that the $\sigma^2$-${\cal M}_s$ relationship is derived, via MHD simulations, for the 3D density variance only, which is not a direct observable. We investigate the utility of a 2D column density $\sigma_{\Sigma/\Sigma_0}^2$-${\cal M}_s$ relationship using solenoidally driven isothermal MHD simulations and find that the best fit follows closely the form of the 3D density $\sigma_{\rho/\rho_0}^2$-${\cal M}_s$ trend but includes a scaling parameter $A$ such that: $\sigma_{ln(\Sigma/\Sigma_0)}^2=A\times ln(1+b^2{\cal M}_s^2)$, where $A=0.11$ and $b=1/3$. This relation is consistent with the observational data reported for the Taurus and IC 5146 molecular clouds with $b=0.5$ and $A=0.16$ and $b=0.5$ and $A=0.12$, respectively. These results open up the possibility of using the 2D column density values of $\sigma^2$ for investigations of the relation between the sonic Mach number and the PDF variance in addition to existing PDF sonic Mach number relations.

Modelling CO emission - I. CO as a column density tracer and the X factor in molecular clouds

Theoretical and observational investigations have indicated that the abundance of carbon monoxide (CO) is very sensitive to intrinsic properties of the gaseous medium, such as density, metallicity, and the background UV field. In order to accurately interpret CO observations, it is thus important to understand how well CO traces the gas, which in molecular clouds (MCs) is predominantly molecular hydrogen (H2). Recent hydrodynamic simulations by Glover & Mac Low have explicitly followed the formation and destruction of molecules in model MCs under varying conditions, confirming that CO formation strongly depends on the cloud properties. Conversely, the H2 formation is primarily determined by the age of the MC. We apply radiative transfer calculations to these MC models in order to investigate the properties of CO line emission. We focus on integrated CO (J=1-0) intensities emerging from individual clouds, including its relationship to the total, H2, and CO column densities, as well as the "X factor," the ratio of H2 column density to CO intensity. Models with high CO abundances have a threshold CO intensity ~65 K km/s at sufficiently large extinctions. Clouds with low CO abundances show no such intensity thresholds. The distribution of H2 column densities are well described as log-normal functions, though the distributions of CO intensities and column densities are usually not log-normal. In general, the PDFs of the integrated intensity do not follow the distribution functions of CO column densities. In the model with Milky Way-like conditions, the X factor is in agreement with the near constant value determined from observations. In clouds with lower CO abundances the X factor can vary appreciably - sometimes by > 4 orders of magnitude. In models with high densities, the CO line is fully saturated, so that the X factor is directly proportional to the molecular column density.

Heavy water around the L1448-mm protostar

Context: L1448-mm is the prototype of a low-mass Class 0 protostar driving a high-velocity jet. Given its bright H2O spectra observed with ISO, L1448-mm is an ideal laboratory to observe heavy water (HDO) emission. Aims: Our aim is to image the HDO emission in the protostar surroundings, the possible occurrence of HDO emission also investigating off L1448-mm, towards the molecular outflow. Methods: We carried out observations of L1448-mm in the HDO(1_10-1_11) line at 80.6 GHz, an excellent tracer of HDO column density, with the IRAM Plateau de Bure Interferometer. Results: We image for the first time HDO emission around L1448-mm. The HDO structure reveals a main clump at velocities close to the ambient one towards the the continuum peak that is caused by the dust heated by the protostar. In addition, the HDO map shows tentative weaker emission at about 2000 AU from the protostar towards the south, which is possibly associated with the walls of the outflow cavity opened by the protostellar wind. Conclusions: Using an LVG code, modelling the density and temperature profile of the hot-corino, and adopting a gas temperature of 100 K and a density of 1.5 10^8 cm^-3, we derive a beam diluted HDO column density of about 7 10^13 cm^-2, corresponding to a HDO abundance of about 4 10^-7. In addition, the present map supports the scenario where HDO can be efficiently produced in shocked regions and not uniquely in hot corinos heated by the newly born star.

THE “TRUE” COLUMN DENSITY DISTRIBUTION IN STAR-FORMING MOLECULAR CLOUDS

We use the COMPLETE Survey's observations of the Perseus star-forming region to assess and intercompare three methods for measuring column density in molecular clouds: extinction mapping (NIR); thermal emission mapping (FIR); and mapping the intensity of CO isotopologues. The structures shown by all three tracers are morphologically similar, but important differences exist. Dust-based measures give similar, log-normal, distributions for the full Perseus region, once careful calibration corrections are made. We also compare dust- and gas-based column density distributions for physically-meaningful sub-regions of Perseus, and we find significant variations in the distributions for those regions. Even though we have used 12CO data to estimate excitation temperatures, and we have corrected for opacity, the 13CO maps seem unable to give column distributions that consistently resemble those from dust measures. We have edited out the effects of the shell around the B-star HD 278942. In that shell's interior and in the parts where it overlaps the molecular cloud, there appears to be a dearth of 13CO, likely due either to 13CO not yet having had time to form in this young structure, and/or destruction of 13CO in the molecular cloud. We conclude that the use of either dust or gas measures of column density without extreme attention to calibration and artifacts is more perilous than even experts might normally admit. And, the use of 13CO to trace total column density in detail, even after proper calibration, is unavoidably limited in utility due to threshold, depletion, and opacity effects. If one's main aim is to map column density, then dust extinction seems the best probe. Linear fits amongst column density tracers are given, quantifying the inherent uncertainties in using one tracer (when compared with others). [abridged]

Infrared Excess Sources in the Canadian Galactic Plane Survey

Using data sets from the Canadian Galactic Plane Survey, we have conducted a multiwavelength study of interstellar components, covering the region 102.5° < l < 141.5° and -3.03° < b < 5.41°. By comparing column density tracers of dust, atomic hydrogen, and molecular gas (traced by CO emission), we have found regions where the dust optical depth shows evidence of more gas than is predicted by the H I and CO observations. Within this population of infrared excess sources, it is possible to discriminate between sources associated with low and high dust temperatures. We interpret the colder temperature sources as molecular clouds/clumps not traced by the CO J = 1-0 transition. Possible reasons include the depletion of CO onto dust grains in the coldest, densest regions of molecular clouds, or photodissociation of CO on the outskirts of molecular clouds.

High-resolution mapping of interstellar clouds with near-infrared scattered light

Context. With current wide-field near-infrared (NIR) instruments the scattered light in the near-infrared can be mapped over large areas. Below $A_{\rm V}\sim 10$ mag the surface brightness is directly proportional to the column density, and at slightly higher column densities the saturation of the intensity values can be corrected using the ratios of the intensity in different NIR bands. Therefore, NIR scattered light provides a promising new method for the mapping of quiescent interstellar clouds. Aims. We develop a method to convert the observed near-infrared surface brightness into estimates of the column density. We study and quantify the effect that different error sources could have on the accuracy of such estimates. We also propose to reduce systematic errors by combining surface brightness data with extinction measurements derived from the near-infrared colour excess of background stars. Methods. Our study is based on a set of three-dimensional magnetohydrodynamic turbulence simulations. Maps of near-infrared scattered light are obtained with radiative transfer calculations, and the maps are converted back into column density estimates using the proposed method. The results are compared with the true column densities. Extinction measurements are simulated using the same turbulence simulations, and are used as a complementary column density tracer. Results. We find that NIR intensities can be converted into a reliable estimate of the column density in regions with A V up to almost 20 mag. We show that the errors can be further reduced with detailed radiative transfer modelling and especially by using the lower resolution information available through the colour excess data. Conclusions. We urge the observers to try this new method out in practice.

The COMPLETE Survey of Star-Forming Regions: Phase I Data

We present an overview of data available for the Ophiuchus and Perseus molecular clouds from ``Phase I'' of the COMPLETE Survey of Star-Forming Regions. This survey provides a range of data complementary to the Spitzer Legacy Program ``From Molecular Cores to Planet Forming Disks.'' Phase I includes: Extinction maps derived from 2MASS near-infrared data using the NICER algorithm; extinction and temperature maps derived from IRAS 60 and 100um emission; HI maps of atomic gas; 12CO and 13CO maps of molecular gas; and submillimetre continuum images of emission from dust in dense cores. Not unexpectedly, the morphology of the regions appears quite different depending on the column-density tracer which is used, with IRAS tracing mainly warmer dust and CO being biased by chemical, excitation and optical depth effects. Histograms of column-density distribution are presented, showing that extinction as derived from 2MASS/NICER gives the closest match to a log-normal distribution as is predicted by numerical simulations. All the data presented in this paper, and links to more detailed publications on their implications are publically available at the COMPLETE website.

Cloudshine: New Light on Dark Clouds

We present new deep near-infrared images of dark clouds in the Perseus molecular complex. These images show beautiful extended emission that we model as scattered ambient starlight and name cloudshine. The brightness and color variation of cloudshine complicates the production of extinction maps, the best tracer of column density in clouds. However, since the profile of reflected light is essentially a function of mass distribution, cloudshine provides a new way to study the structure of dark clouds. Previous work has used optical scattered light to study the density profile of tenuous clouds; extending this technique into the infrared provides a high-resolution view into the interiors of very dense clouds, bypassing the complexities of using thermal dust emission, which is biased by grain temperature, or molecular tracers, which have complicated depletion patterns. As new wide-field infrared cameras are used to study star-forming regions at greater depth, cloudshine will be widely observed and should be seen as a new high-resolution tool, rather than an inconvenience.

Models for Interstellar Extinction in the Galaxy

We present two models for the interstellar extinction in the Galaxy that are based on the hypothesis that the interstellar dust is well mixed with the gas, with a constant ratio (except for a small dependence of metallicity on the Galactic radius), and therefore that the extinction is proportional to the column density of the gas. In the first model we assume that the Galaxy is axisymmetric; the gas density in the disk is a function of the Galactic radius and of the distance perpendicular to the Galactic plane, and the extinction is proportional to the column density of the gas. In the second model we take into account the spiral structure of the Galaxy. In this case, instead of increasing almost linearly with distance, the extinction increases by steps each time a spiral arm is crossed, but only increases slowly in the interarm regions. The gas density distribution is obtained from the Berkeley and Parkes H I surveys and from the Columbia University CO survey. The IRAS 100 μm brightness distribution is also used as a tracer of the interstellar dust column density. The predictions of the models are compared with data taken from a number of catalogs that present color excess and distances for large samples of stars. Our models are useful for estimating distances of objects and color corrections for objects for which the distance can be estimated by some other method, and also for star counts and brightness models of the Galaxy, among other applications.