INVESTIGATING EXTINCTION PROPERTIES OF BOK GLOBULES WITH THE SARA 0.9M TELESCOPE

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1 Journal of the Southeastern Association for Research in Astronomy, VOL, 00-00, DATE c Southeastern Association for Research in Astronomy. All rights reserved. INVESTIGATING EXTINCTION PROPERTIES OF BOK GLOBULES WITH THE SARA 0.9M TELESCOPE Andrew M. Johnson 1, Adria Updike 1, Dieter H. Hartmann 1 Department of Physics and Astronomy, Clemson University, South Carolina, ABSTRACT Extinction effects are ubiquitous in the interstellar medium of galaxies. In particular, extinction due to molecular clouds can significantly change the color and brightness of background or embedded objects. The structure of molecular clouds is an important observable, relevant for the initial conditions under which star formation takes place. Mapping the effects of extinction across a molecular cloud can be used to deduce its internal structure. We present such an analysis for several Bok Globules which we observed with the 0.9m SARA telescope at Kitt Peak National Observatory. In particular, we investigate the structure of CB188, whose geometry is such that it can be approximated by a spherical model. We find that the model for a globule with a constant density profile is inconsistent with what we observe; this solution has led up to explore other models with more complex density structures. Subject headings: Bok Globules, extinction, color-index, reddening. 1. INTRODUCTION Bok Globules are relatively small, isolated, dense molecular cloud cores believed to be regions of potential star formation. Current models of these objects suggest their radii to be on the order of several thousand A.U., with masses ranging from 0.5 to 8 M and very low temperatures of about 10 K (Kandori et al. 2005). They owe their name to astronomer Bart Bok, who in his original paper titled Small Dark Nebulae received on January 10th 1947, presents the measured angular distances of small dark objects against the luminous background of Messier 8, also known as the Lagoon Nebula (Bok & Reilly 1947). In this early work, the derived linear dimensions of the globules were in the range between 7,000 to 80,000 AU which agrees with current models of these dense cores. Furthermore, Bok also suggested that these small dark nebulae probably represent the evolutionary stage just preceding the formation of a star. This interpretation is the currently accepted point of view (e.g., Stahler & Palla 2005). To investigate the interior structure of these clouds one can utilize optical to nearinfrared photometry of stars located behind them. In particular, clouds that are nearby, and thus have very low probabilities for stars in the foreground are useful for this study. In addition, one seeks isolated clouds, i.e., those in which stars have not yet been formed because this avoids complexities induced by the radiation field of embedded stars. To model the current structure of these molecular cloud cores and to determine their future dynamical evolution one must obtain an estimate of their total mass, and if possible, the spacial density distribution. Approximating a cloud with a spherical model thus implies the need to determine the radial density profile. If these clouds are nearly in hydrostatic equilibrium, their density profile is surely not that of a uniform sphere. However, we shall consider homogeneous spheres as an initial guess. Besides the density, one would ideally obtain in- 1 Southeastern Association for Research in Astronomy (SARA) NSF-REU Summer Intern Electronic address: andrew7@clemson.edu formation about abundances of the various elements, the fraction of molecular gas, the ratio of dust to gas, and other properties such as temperature and pressure. Under the assumption of a standard dust to gas ratio, one can utilize the dust in these clouds as a tracer of the overall density. Viewing the field of background stars across a globule reveals the dust column density due to the effect of extinction and reddening; which can then be converted to a total mass column density, and in turn to a density profile under the assumption of a given geometry (going from the simplest model of a uniform sphere of a more realistic distribution following the Bonnor-Ebert model). This approach was successfully carried out by several groups; Alves et al. (2000), Alves (2004), Alves et al. (2007), and Kandori et al. (2005). A stability analysis was performed for 10 Bok Globules by Kandori et al. (2005) using the Bonnor-Ebert sphere model. These authors find that CB188, the primary object of study in this work is in fact unstable, and provide evidence for the presence of a protostar embedded in the cloud (Kandori et al. 2005). This paper is organized as follows: in Section 2 we present the observations used in this study. Section 3 discusses the basic effects of dust on radiation transport. Data analysis and statistical interpretations are presented in Section 4, and the implications based on special distribution models are discussed in Section 5. Conclusions are drawn in the final section. 2. OBSERVATIONS AND DATA REDUCTION Observations of 4 Bok Globules (CB188, C8134, CB87, and FEST 1-457) were taken using the SARA 0.9m telescope on June 11th-12th at Kitt Peak National Observatory in Arizona. Exposures were taken using the Apogee Alta CCD with 2x2 binning. Exposure times for each image were 200s and exposures were taken in the Bessel V, R, and I filters. Each image was dark subtracted, bias corrected, and flat fielded using the ccdproc task in IRAF (Image Reduction Analysis Facility). No fringing correction was made to the I band due to the lack of sufficiency dithered images; however, as the fringes only contribute a few percent of the flux above the background

2 Extinction Effects of Bok Globules 1 level, we do not consider this to be a major problem for this analysis. The images were then stacked in IRAF according to filter, and master image frames were obtained for the clouds in each band. Figure 1, 2, 3 show the stacked images in each band for the objects of interest. Fig. 3. Calibrated and stacked images of CB188 in the I band. corresponds to a total 100,000 stars within a distance of 300 pc distributed uniformly on the sky. Fig. 1. Calibrated and stacked images of CB188 in the V band. Fig. 2. Calibrated and stacked images of CB188 in the R band. All of the observed clouds are located toward the mid plane of the Milky Way and are estimated to be within 300 parsecs of the sun or less. The low galactic latitudes of each cloud cause a high density of background stars, but their proximity implies very few to no foreground stars. In the solar neighborhood the density of stars is about 1 per cubic parsec (some reference) which 3. METHODS In order to discuss extinction and its usefulness in surveying Bok Globules we define the color-index and its relation to physical quantities, in particular, the optical depth of the cloud. Extinction is the combined effect of scattering and absorption of light due to interstellar matter. One expresses the extinction in terms of magnitudes (Aλ ), or in terms of the optical depth (τλ ), both of which are dimensionless measures of how opaque the medium along the line of sight is at a given wavelength. In fact, both quantities are directly related to each other, which we will show later. Many different types of scattering and absorption processes can occur, all with the common end result that the light does not reach our detectors. However, although this effect is a setback in the sense that it reduces the observed flux of the object, it is useful in deriving some properties of the intervening medium. Starlight may be completely extincted on its journey from a source through a cloud along the line of sight resulting in a dark, visibly opaque hole in the sky as William Herschel called them. Extinction in the visible part of the electromagnetic spectrum is dominated by scattering of light of the dust particles residing in the interstellar medium. The underlying particle-radiation interaction results in much less extinction at longer wavelengths, i.e., the ISM is much more transparent in the infrared region than in the optical band, while the ultraviolet part of the spectrum is much more opaque. This implies that observations of a background field of stars through an opaque cloud will result in an optical hole but possibly reveal the background stars in the infrared. In other words, star counts in the NIR will detect significantly greater numbers of stars behind the cloud in contrast to observations in the optical bands. In addition to affecting star counts, one can also probe the intervening cloud through the wavelength depen-

3 2 A. M. Johnson & A. Updike & D. Hartmann dence of extinction. In other words, studying the effects of reddening across the cloud is another measure of the extinction properties and thereby the physical properties of the cloud. To quantify this approach, one analyzes the color index of stars behind a molecular cloud to show that their spectral energy distributions (SEDs) have been reddened. Since scattering of light is dependent on wavelength of radiation and the size of the particle responsible for scattering, the observation of reddening (in principle) provides information on the particlesize distribution and the size of the particles. Interstellar dust grains have a size range from around 0.1 to 1 µm, with a power law probability density that describes a much higher probability for small grains (Mathis et al. 1977). Since dust particles also absorb light, they must attain equilibrium temperatures in the range of K, depending on the source of the light responsible for heating them. These warm dust particles are thus also sources of light by means of thermal blackbody radiation from their surfaces. Since the dust is rather cold (the temperature of the cosmic microwave background 2.7 K) the emission from dust predominantly falls in the window of the long wavelength band on the order of 100 µm. To quantify the reddening effects due to scattering of interstellar dust, we now proceed to with the definition of the color index Color-Temperature Relationship The color index is the difference between the magnitudes of a star in two separate filters. Since the magnitude is defined by the flux in a given band, the difference of two magnitudes corresponds to the logarithm of the ratio of the fluxes when integrated over the filter. For example, if we integrate the SED (f λ, the flux density) over the filter function in the B band we obtain the flux specific to that range of wavelengths. Since the fluxes that we are interested in are specific in wavelength, we must integrate the SED (spectral energy distribution) over a filter function characterized by the filter we want the magnitude to be measured in. Let us take the B band as an example: f B = 0 f(λ)φ B (λ)q(λ)dλ (1) where φ B (λ) is the B band filter function and Q(λ) is the quantum efficiency of the detector, which for simplicity we are assuming to be one hundred percent, i.e., Q = 1. If we assume that filters are very narrow, we can approximate the filter function with a Dirac delta function δ for the flux over that particular range of wavelengths so that the flux will be evaluated at the specific wavelength of interest (λ o ). In the above example, λ o = λ B = 550 nm. Furthermore, if we assume stellar SEDs to be perfect blackbody spectra, and employ the standard definition of magnitude (M = 2.5 log(f λ ) + C), we obtain a color index derived from the B and V band to be ( ) fb B V = 2.5 log + C (2) where f B = 1 λ 5 B f V 1 e hc/λ BkT 1, f V = 1 λ 5 V 1 e hc/λ V kt 1 (3) for the B and V bands, respectively. We place the delta function at the wavelengths where these filters have maximum transmission, i.e., λ V = 440 nm, λ B = 550 nm. With these assumptions, we numerically evaluate the color index s dependence on temperature. A further simplification is found if we assume that the temperatures are lower than 10,000 K because the exponential term in the denominator is significantly larger than unity. In this approximation the color index reduces to B V = T (K) + C (4) We have thus obtained the B V color index as a function of temperature and can similarly derive color indices based on other filter combinations; however, the constant in the above equation has not yet been determined. We determine this constant by using the known solar color index of B V = in conjunction with the solar temperature of T = 5770 K (Holmberg et al. 2006). With this solar calibration, we obtain the B V color index as a function of temperature B V = T (K). (5) The color index-temperature relationship obtained in the two approximations described above is shown in Figure 4. We emphasize that the use of the Dirac delta function as a substitute for actual filter functions is a rather severe approximation to the problem. However, these relationships will be sufficient to guide our interpretation of reddening as described in terms of optical depth in the next section. The color index is a dimensionless quantity derived from the ratio of fluxes in two separate bands. If the color index is defined as stated above, i.e., magnitude at shorter wavelengths minus magnitude at longer wavelengths, then a larger color index indicates a redder object. In the absence of intervening dust, a redder color indicates a lower temperature. Since the effects of dust are dimming as well as reddening, ignoring extinction corrections would lead to the false impression of a reduced temperature of the object under investigation. From Figure 4, we see that the B V color index is not a sensitive measure of temperature for stars much hotter than 10 4 K. For these stars, other bands can be used. This photometric approach to measuring temperature is described in detail in Kitchin (1998) Correction for Reddening Another dimensionless quantity characterizing the wavelength-dependent extinction due to intervening material is the optical depth τ λ of the medium. The flux density observed from an object at a distance D; f λ is exponentially suppressed according to the relation where the optical depth is given by τ λ = D 0 f λo = f λ e τ λ (6) σ(λ)n(x)dx = Σ d σ(λ)d. (7) In this integral along the line of sight, σ(λ) is the wavelength dependent scattering cross section and n(x) is the

4 Extinction Effects of Bok Globules 3 The correct temperature of the object can now be inferred from the observed color index (B V ) o if the optical depth of the intervening medium is known. Likewise, if the intrinsic color is known, the observed color index allows a determination of the optical depth. Carrying out such measurements for various stars at different distances then allows one to obtain the average extinction per unit distance in the ISM near the Sun. A commonly used value is 1 2 magnitudes per kpc in the V band. If this value were constant throughout the entire galactic disk, objects near the galactic center would experience about magnitudes of extinction, corresponding to a reduction of flux by a factor of 10 4 for 10 magnitudes and 10 8 for 20 magnitudes. One would hardly be able to observe stars near the galactic center in the V band. Fortunately, the scattering cross section is a sensitive function of wavelength, being much lower in the infrared part of the spectrum. Observations of stars in the core of the Milky Way are thus the objective of infrared astronomy. The wavelength dependence of extinction (measured by either A λ or τ λ ) is shown in Figure 5. It is clear to see that with shorter wavelengths, extinction is very high and decreases out to the longer wavelengths. For an assumed extinction of 1 magnitude in the V band (using Figure 5) the observed color index is shown in comparison to the color index as a function of temperature in Figure 6. Fig. 4. B V color index. This curve is normalized to the value of solar (B V ) and only holds under the assumption that the filter is a delta function. number density of dust particles as a function of position along the line of sight. The second part of this equation results from separating out the universal cross section, leaving the line of sight integral of the number density, which is referred to as the dust particle column density. Since magnitudes are proportional to the logarithm of flux (see Equation 4), the conversion between optical depth (τ λ ) and magnitudes of extinction (A λ ) is given by τ λ = 0.4A λ log e. (8) The flux of a source is reduced by extinction as the light passes through the ISM or a particular cloud within the ISM. The resulting color index will increase, reflecting the reddening effect of the medium. Using the above equations to modify the fluxes that appear in the definition of the color index (see Equation 4) thus results in the observed color index (during this process one finds an extra term is added which increases the color index, making the colors redder ). Namely, the color index is increased with increasing values of τ V. The corrected color index is shown in Equation 9, (B V ) o = (B V )(T ) + (τ B τ V ) log e. (9) Fig. 5. A λ as a function of wavelength, given in magnitudes. Normalized so that A V = 1, in the V band. Stars mark the wavelengths of filters UBV RIJHK. This is a quantitative interpretation of the reddening effect; the increase in color index suggests a redder source which is indistinguishable if the intrinsic colors of the source are unknown. Our previous B V color index is shown in Figure 6 after it has been corrected for an extinction of A V = 1. Fig. 6. B V color index as a function of temperature, and the same color index corrected for an extinction of A V = RESULTS As discussed in the previous sections, an analysis of the density structure of an assumed spherically symmetric dark cloud can be carried out either through the dimming effect (reduced star count), or the reddening effect

5 4 A. M. Johnson & A. Updike & D. Hartmann (changing color index as a function of position in the image). Colors: The magnitudes for stars in the calibrated and stacked images are obtained in the V, R, I band with aperture photometry as implemented in IRAF. The instrumental magnitudes obtained in this process were then calibrated using field stars taken from the USNO B1.0 (in R,I) and NOMAD (in V ) catalogs. The uncertainties of the brightness measurements through relative aperture photometry can be determined with standard statistical techniques, but we note that the systematic uncertainties might dominate the case at hand because of the crowded field near the galactic plane. A proper error analysis would best be performed after replacing aperture photometry with a detailed point spread function analysis. Putting aside issues related to error analysis, we show the distribution of stars as a function of brightness (number of stars per magnitude bin, using a bin width of 0.5 magnitudes). These results indicate that the sample of stars is complete to magnitude limits of V lim 20, R lim 19, I lim 18. Above the completeness limit, we find that the number of stars for which magnitudes were determined is 1000 in V, 1500 in R, and 2000 in I. For a variety of reasons, including the apparent effect of extinction due to CB188 and other globules in this field, the number of detected stars in the I band is significantly larger than those at shorter wavelengths. Fig. 7. V,R,I magnitudes obtained through aperture photometry. Many more stars can be viewed in the infrared (I) band as opposed to the visual band. Using the magnitudes from each of the stacked images through the V, R, and I filters, color-color diagrams were constructed for all stars with established magnitudes in all three bands. These results are shown in Figure 8. The vast majority of these stars are unaffected by dust reddening while a small subset would experience reddening due to CB188; however, stars for which the reddening effect is strongest (stars closest to the cloud) may be detected in the I band but not in one or both of the other bands. Consequently those stars for which the reddening effect we seek to analyze is strongest are not contained in the color-color plot simply because the needed information (V, R, and I magnitudes) are not available. This problem, in conjunction with the overall uncertainties in the aperture based photometric colors, renders this approach unfeasible. To overcome these problems, source detection would have to reach much fainter limiting magnitudes (possible with a combination of larger aperture telescopes, ground-based active optics for improved angular resolution, or space-based observations) and extend deeper into the long wavelength part of the spectrum. We thus abandon this approach and consider the second alternative based on star counts. Fig. 8. Color-color diagram showing R I against V R. Star counts: In order to perform a statistical analysis of the number density of stars across the image, we used SExtractor (Bertin & Arnouts 1996) to obtain pixel coordinates for each cloud image. As discussed above, we focus mainly of the images of CB188 due to its less populated star field and apparent spherical shape. The task of extracting sources requires algorithms that identify pixels in an image whose distribution is consistent with the point spread function of the image. This process is sensitive to the selection of a threshold parameter that determines a detection criterion. We applied SExtractor multiple times on each image to find the threshold value for which as many sources as possible could be reliably determined. If the threshold is too low, the source list obtained by sextractor would become noise-dominated. For each detected source, SExtractor determines the centroid of the count distribution, thus providing a relative position on the CCD image with an accuracy better than one pixel. Using ds9, we circled each star detected by SExtractor. We inspected these embellished images by eye to determine an optimal threshold. We find that using a 0.8σ detection threshold level worked best to both locate faint but detected stars and eliminate non-stellar sources. Based on the locations (x and y coordinates on the CCD chip) one can create an image of dots corresponding to the image of counts shown in Figures 1, 2, and 3. Figure 9 shows the R band image as an example. This figure reveals two empty regions, one in the center (the part of the background blocked by CB188), the other located in the north west, near the edge of the chip caused by a nearby bright star blocking sextractor from identifying faint sources in its vicinity. The star count technique relies on measuring the surface density of stars in a given band as a function of position within the image. We created a smooth density map (shown in Figure 10) by sliding a square window across the image. The window size must be small compared to the dimension of the full image, but large enough to mostly contain more than just a few stars to minimize statistical fluctuations. Figure 10 shows the result of this procedure using a 50x50 pixel window moved with a step length of

6 Extinction Effects of Bok Globules 5 10 pixels. We used IDL s contour command to overlay lines of constant stellar surface density. As is apparent from the original CCD image, the star density does not vary substantially across the field of view with the exception of the areas blocked by CB188. As expected, the emerging hole in the sky is smallest at long wavelengths. This wavelength dependence of the radius of the cloud is the diagnostic we will use to infer the density structure of the cloud. We determined the radius from a visual inspection of the image, identifying the common center of the cloud and defining the radius such that no more than 10% of the area contains stars. The resulting density as a function of position is given in Figure 10. Fig. 9. Pixel coordinates of each detected source using SExtractor in the V band. Fig. 10. V,R,I contour plots for CB188. With V at the top, then R, and last I. The extent of the hole in the sky is expected to be largest at the shortest wavelengths. We thus select the V band image to determine the geometric center of the hole through visual means. This center is then applied to all images. In each image, we determine the circle of maximum radius that fits within the hole. The radius of that circle as a function of wavelength is shown in Figure 11. As expected, the size of the hole shrinks with increasing wavelength. Although only three radius measurements are obtained by this method, it might still be possible to derive or at least constrain the actual density profile of the cloud. This modeling task is described in the next section. 5. MODELS We have already argued in favor of the simplifying assumption that CB188 is spherically symmetric. Let us furthermore assume that we are dealing with a homogeneous sphere. For the purpose of extinction calculations, this sphere is characterized by the maximum optical depth corresponding to a line of sight through the center. Fig. 11. Radius (given in pixels) of the cloud as a function of wavelength. These results are from our common center-circle method of measuring the apparent decrease in radius at long wavelengths. (10) function of radius r (projected distance from the center of the cloud) is given by We select the V band as the point of reference so that a selection of τvmax determines its analog values in the R and I bands using the extinction curve, Figure 5. Due to the simple geometry and the assumption of the constant density, the total optical depth through the cloud as a r 21 τλmax = τ max 1 (11) R where R is the true radius of the cloud. It is common to assume that τ = 1 is the dividing line, albeit a very fuzzy line, separating the opaque and trans- τλmax = 2 Z R σ(λ)n(x)dx = 2nσ(λ)R 0

7 6 A. M. Johnson & A. Updike & D. Hartmann parent regimes. With this assumption, the observed wavelength-dependent radius of the hole is determined by [ (τ max ) 2 ] r = R (τ max ) 2. (12) unstable. Our measurements of the color dependent radius of the hole clearly indicated that the density is not constant and the hydrostatic equilibrium models suggest a strongly radius-dependent density in the outer layers. Since our observations only probe the outer parts of the cloud, another class of models worthy of investigation are density profiles of power-law type. This study is the subject of a forthcoming investigation. Fig. 12. Fractional radii as a function of wavelength. For smaller radii, the cloud is assumed opaque (τ > 1). Outside, it is transparent. This agrees with what we know about the wavelength dependence of extinction as well as furthers our curiosity as to what the actual density profile of the cloud is. For this we must use the Bonnor-Ebert sphere model Bonnor-Ebert Sphere Model Bok globules are believed to be the dense and cold molecular regions that are either in hydrostatic equilibrium or unstable and in the process of collapsing to become a protostar. Balance between gravitational forces and pressure leads to a configuration in hydrostatic equilibrium. The density structure for such a cloud can be obtained as a solution to the Bonnor-Ebert Ebert (1955); Bonnor (1956) differential equation, 1 ξ 2 d dξ ( ξ 2 dφ dξ ) = e φ (13) where ξ max is a radius variable and φ denotes the gravitational potential. This model gives us a density profile for an isothermal spherical cloud in hydrostatic equilibrium. The model assumes that the density of the object is not homogenous, but falls off with radius according to.. The numerical integration of the equation (e.g., Kandori et al. 2005), shows that the density profile is flat near the center but changes to a ρ r 2 behavior in the envelope. This sphere is characterized by a dimensionless parameter which measures its stability against gravitational collapse (ξ max ). Kandori et al. (2005) interpreted CB188 with a Bonnor-Ebert sphere as the underlying density model and conclude that it is in fact 6. DISCUSSION AND CONCLUSIONS Based on our observations with SARA, we found that with longer wavelengths, the apparent size of so called globules appears to shrink. This effect is straightforward to interpret in terms of dust extinction in the cloud, and would be even more noticeable in near-infrared images. We considered two techniques to investigate the structure of these clouds; color changes (reddening) across the cloud and changes in number density as a function of wavelength (star counts). Due to the crowded nature of these low galactic latitude fields, the color method rendered itself unusable, while the star count method allowed us to derive a apparent size-wavelength relationship. Under certain circumstances the color excess technique can be made to work (Krelowski & Papaj 1993), but in this study we limited the investigation to the star count method. Modeling globules as homogeneous spherical clouds reproduces the shrinking with increasing wavelength trend but does not reproduce the shape of this relationship. Non-uniform density spheres (Bonnor-Ebert spheres or simpler models with power-law density structures) could reduce this discrepancy and ultimately serve as a probe of structure. A further complication can occur when Bok Globules are not starless but may contain protostellar sources within them. Based on infrared data (Harvey et al. 2003) it was established that protostellar cores have very high column densities corresponding to extinctions in excess of (A V > 40). Near infrared observations by Lada et al. (2007) and Kandori et al. (2005) have demonstrated that even compact, high column density cores can be penetrated in the H band (1.65µm) and K band (2.2µm). To probe the density profiles of these star forming condensations in the ISM, near-ir and IR observations are required. Further insight into the structure of these molecular cloud cores can be obtained by radio observations, as discussed by Kandori et al. (2005). An extension of this study utilizing observations obtained in the 2MASS (2 Micron All Sky Survey) data set is underway. This project was funded by the National Science Foundation Research Experiences for Undergraduates (REU) program through grant NSF AST A special thanks to Aman Kaur for assistance with IRAF software. The manuscript was prepared according to the style format given at Alves, J., Lombardi, M., & Lada, C. J. 2007, A&A, 462, L17 Alves, J. 2004, Ap&SS, 289, 259 REFERENCES Alves, J., Lada, C., & Lada, E. 2000, Star Formation from the Small to the Large Scale, 445, 157

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