Molecular cloud distance determination from deep NIR survey extinction measurements
aa r X i v : . [ a s t r o - ph . GA ] M a y Mon. Not. R. Astron. Soc. , 1–18 (2002) Printed 20 November 2018 (MN L A TEX style file v2.2)
Molecular cloud distance determination from deep NIRsurvey extinction measurements
J.J. Stead ⋆ , M.G. Hoare ⋆ School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT
ABSTRACT
Using near infrared UKIDSS Galactic Plane Survey data, we make extinction mea-surements to individual stars along the same line of sight as molecular clouds. Usingan existing 3D extinction map of the inner Galaxy, that provides line of sight specificextinction-distance relationships, we convert the measured extinction of molecularclouds to a corresponding distance. These distances are derived independently fromkinematic methods, typically used to derive distances to molecular clouds, and as suchthey have no near/far ambiguity. The near/far distance ambiguity has been resolvedfor 27 clouds and distances have been derived to 20 clouds. The results are found tobe in good agreement with kinematic measurements to molecular clouds where theambiguity has already been resolved, using HI self-absorption techniques.
Key words: (ISM:) Interstellar Medium (ISM): dust, extinction
Molecular clouds are the birth places of massive stars.They form in an environment shielded from Galactic radia-tion and so their cold temperatures allow the formation ofH . Star formation is triggered through gravitational insta-bility inside the cloud, when a cloud fragment’s gravitationalenergy exceeds its internal energy. As massive star formingregions are retentive of their natal cloud, until it is dispersedby the formation of HII regions, if the distance is known tothe molecular cloud, then the distance is known to the mas-sive star forming region.The Red MSX Source (RMS) survey (Urquhart et al.2008) has carried out a series of multi-wavelength followup observations, to identify genuine massive young stel-lar objects (MYSOs), and ultra compact (UC) HII regions.Initially, a large sample of MYSO candidates were colour-selected from the MSX point source catalogue (Egan et al.2003) by Lumsden et al. (2002). To confirm the presence ofa massive young star, we need to determine the luminosityof each source. Thus, we need an accurate measurement ofeach MYSO candidate’s heliocentric distance.Every MYSO candidate in the RMS survey has hada kinematic distance determined, from CO observations(Urquhart et al. 2008), to the molecular cloud from whichit was formed. Kinematic distances are derived by applying ⋆ E-mail: [email protected]; [email protected] a Galactic rotational model to measured kinematic veloc-ities. Excluding localised velocity perturbations, the kine-matic velocity is the projection of the orbital velocity of amolecular cloud, about the Galactic centre, along the line ofsight. Therefore for clouds within the Solar circle, there isnot a unique solution to the derived distance and such cloudswill possess a near/far kinematic ambiguity. Urquhart et al(in prep.) have used a recent catalogue of molecular clouds(Rathborne et al. 2009) to identify the molecular cloudsmost likely associated with RMS sources. Using HI self-absorption and also absorption towards 21 cm continuumsources embedded in molecular clouds, Roman-Duval et al.(2009) resolved the near/far ambiguity to ∼
90% of all molec-ular clouds identified by Rathborne et al. (2009). Using datafrom Roman-Duval et al. (2009), Urquhart et al (in prep.)have resolved the kinematic ambiguity to 186 RMS sources.Kinematic distance ambiguities, although shown to besolvable by Roman-Duval et al. (2009), are not the only po-tential pitfall when attempting to derive distances to molec-ular clouds using kinematic techniques. The conversion ofkinematic velocities into kinematic distances requires an ac-curate Galactic rotation model, and the assumption thatthe measured kinematic velocity is due entirely from rota-tion about the Galactic centre. Kinematic velocities inferdistances of ∼ ∼ ± c (cid:13) have been found to 18 masers by Reid et al. (2009), but par-allax measurements are still sparse. Clearly there is much togain from any distance determination method that is inde-pendent to Galactic rotation models.Molecular clouds are very optically thick. As such, starsbehind molecular clouds will suffer much more extinctionrelative to stars in front of molecular clouds along the sameline of sight. Several authors have used extinction mea-surements to perform a wide variety of tasks. Using cu-mulative star counts from 2MASS, Froebrich et al. (2005)have constructed relative extinction maps of the GalacticPlane. Lombardi & Alves (2001) deredden 2MASS data todetermine the near infrared colour excess of stars to pro-duce extinction maps. They deredden all stars to a sin-gle, average intrinsic colour using the reddening vector ofRieke & Lebofsky (1985). Sale et al. (2009) use IPHAS H α data to simultaneously determine extinction, intrinsic colourand distance estimates of early-A to K4 stars. They use thesedata to map extinction in three dimensions across the north-ern Galactic Plane. Marshall et al. (2006) also constructthree dimensional extinction maps of the inner Galaxy using2MASS data and the Stellar Population Synthesis Model ofthe Galaxy, developed in Besan¸con. They used the syntheticBesan¸con data to provide the intrinsic colour and probabledistances of colour selected giant stars, mapping the innerGalaxy in 15 ′ x15 ′ tiles.Using the most reliable United Kingdom Infrared DeepSky Survey (UKIDSS) Galactic Plane Survey (GPS) data,this work dereddens individual giant stars along a particularreddening track, to the point of intersection on an intrinsicgiant locus. The dereddening process allows us to measurethe extinction suffered by stars along the same line of sight asmolecular clouds. We then determine distances, that are in-dependent to Galactic rotation models, to molecular cloudsusing line of sight specific extinction-distance relationships,derived from an existing 3D extinction map of the innerGalaxy. We acquire the 3D extinction map from the previ-ously mentioned Marshall et al. (2006) data. We utilise theUKIDSS GPS to essentially improve the resolution of theMarshall et al. (2006) data by analysing only stars that aresituated directly along the same line of sight as the molecu-lar cloud.In Section 2, we describe the data used to derive thedistance to each cloud, including the photometric data, andthe data used to model the line of sight specific extinction-distance relationships. In Section 3 we discuss how wecolour-colour and colour-magnitude select a specific sampleof stars, of similar spectral type, to determine the line ofsight extinction. In Section 4 we use the line of sight extinc-tion measurements to identify the spatial extent of molecularclouds. In Section 5 we derive, in detail, the distance to twoexample molecular clouds. We derive distances to a further19 molecular clouds and the results are presented in Sec-tion 6. We discuss the results and make comparisons withprevious authors in Section 7. The UKIDSS Galactic Plane Survey (GPS, see Lucas et al.(2008)) covers, in the J(1.248 µ m), H(1.631 µ m) and K(2.201 µ m) filters, the region of the Galactic Plane acces-sible by the United Kingdom Infrared Telescope (UKIRT);15 o < l < o and 141 o < l < o , | b | < o and − o < l < o , | b | < o .The GPS data are obtained from the WFCAM ScienceArchive (Hambly et al. 2008). The median 5 σ depths areJ=19.77, H=19.00 and K=18.05 (Vega system) in the seconddata release of the GPS (Warren et al. 2007). The surveydepth is spatially variable however, typically decreasing lon-gitudinally towards the Galactic centre and latitudinally to-wards the Galactic Plane. This occurs as the fields typicallybecome more crowded towards these regions. Lucas et al.(2008) determine the modal depths in uncrowded fields tobe J=19.4 to 19.65, H=18.5 to 18.75 and K=17.75 to 18.0.It is possible to use several different types of data qual-ity cuts, provided by the WFCAM Science Archive, to selectonly the most reliable data. To do this we remove sourceswith saturated pixels, remove blended objects using ellip-ticity cuts, astrometry cuts remove sources mismatched be-tween different filters, and finally photometric error cuts.The data cuts used in this paper are almost identical tothose presented in Lucas et al. (2008). The only alterationwe make is a photometric error cut of 0.03 mag in eachphotometric filter, whereas Lucas et al. (2008) apply a 0.03mag colour cut. The use of such data quality cuts meansthat the photometric depths of the data used in this paperare reduced to J ∼ ∼ ∼ We utilise the Stellar Population Synthesis Model of theGalaxy, developed in Besan¸con (Robin et al. 2003), to modelthe distribution of giant stars, related to both the distanceand extinction, along specific lines of sight. If an appropri-ate extinction-distance relationship is used to describe theextinction along the line of sight, then as will be shown,comparisons between synthetic and real data can be madeto determine the distance to molecular clouds.A complete description of the Besan¸con model inputscan be found in Robin et al. (2003), however we summariseit here for completeness. The model contains four popula-tions of stars, thin disc, thick disc, bulge and spheroid. Eachof the four populations are described by a star formationrate history, an initial mass function, an age or age range,metallicity characteristics, kinematics, a set of evolutionarytracks, and includes a white dwarf population. The extinc-tion is modelled, in terms of visual magnitudes per kilopar-sec (mag kpc − ), by a diffuse thin disc. It is also possible toinsert discrete clouds with a specified A V and distance. V relationships Marshall et al. (2006) use 2MASS data and the Besan¸conGalactic model to map the Galactic interstellar extinctiondistribution in three dimensions. This has been done to over64,000 lines of sight, in the inner Galaxy, each separatedby 15 ′ (hereafter referred to as the M06 distributions). Inthis paper we use the M06 data to assess the extinction-distance relationships along specific lines of sight. Using theM06 data, the distribution of synthetic giant population is c (cid:13) , 1–18 olecular cloud distance determination from deep NIR survey extinction measurements modelled by using a set extinction model to describe thethin disc (mag kpc − ) and the insertion of discrete cloudsat specific distances.The M06 data produce reliable 3D extinction maps andso provide good line of sight specific extinction-distance re-lationships. In some cases it is possible to detect, and assigna distance to, large molecular clouds using the M06 dataalone. We use the increased sensitivity of the UKIDSS GPS,in comparison to 2MASS, to improve the spatial resolutionof the M06 data, identifying only stars that are situated di-rectly along the same line of sight as the target molecularcloud. It is essential to know the position and spatial size of eachmolecular cloud in order to identify the stars that are situ-ated directly along the same line of sight. Rathborne et al.(2009) have identified 829 molecular clouds in the CO J=1-0 Galactic Ring Survey (GRS Jackson et al. 2006), listingthe Galactic position and the longitudinal and latitudinalFWHM of each cloud. The GRS covers a range of Galacticlongitudes from 18 o < l < o and | b | < o . The GRS isfully sampled with a pixel size of 22 ′′ . The processed datacubes have a V LSR range from -5 to 135 km s − and a spec-tral resolution of 0.13 km s − for l < o . For larger Galacticlongitudes the V LSR range covers -5 to 85 km s − and thespectral resolution is 0.21 km s − .The GRS data serve two purposes in this paper. Forcomparison with the extinction maps produced in section4.3, and to identify the Galactic position and size of severalclouds in order to determine their distances. > Table 1.
CMD/CCD III extractionData cut Besan¸con UKIDSSAll 6,591 6,638CCD 3,792 3,329CMD 1,339 1,135 to split into two separate branches of data. As the most red-dened stars have to be the most intrinsically bright, thesetwo branches will be primarily composed of late giants andearly dwarfs. As late giants are intrinsically redder thanearly dwarfs, the upper, and therefore redder, branch of datawill be composed of giants, the lower will be composed ofdwarfs.A G0III stellar atmosphere model (Castelli & Kurucz2004) is progressively reddened, using an extinction law of α =2.14 (Stead & Hoare 2009), to create a reddening track,hereafter referred to as a CK04 G0III reddening track, thatsplits the CCD, plotted in Figs. 1 (a and b), into two halves.The upper half contains stars redder, and therefore of a laterspectral type, than G0III. The CK04 G0III reddening trackhas been shifted down the y-axis by ∼ σ errors would allow them to be considered as G0III or latercandidates.As the synthetic Besan¸con data can be considered anaccurate representation of the real UKIDSS data, and theclass and spectral type of each synthetic star is known, wecan estimate the make-up of our final UKIDSS sample. Lategiants have very similar colours to late dwarfs of the samespectral type and therefore the colour-colour cut data willbe contaminated with a large number of late dwarf stars. Asthese stars are faint, they can not be observed through largeamounts of reddening. In colour-colour space the late dwarfsblend with the late giants in the field. In colour-magnitudespace however, there is a clear distinction between giant anddwarf stars. Fig. 1 (c) contains the previously selected sam-ple of G0III and later candidates. Highlighted in black andred, in the synthetic data, are the dwarf and giant stars re-spectively, the remaining blue points consist of subgiants,bright giants and supergiants. The dwarf and giant starsform two clumps of data on the CMD. A black line has beenplaced, by eye, approximately equidistant from each clumpseparating the CMD into two halves. Although a small num-ber of giants are positioned in the first half of the CMD, it issafe to assume that the second half of the CMD is free fromdwarf stars. We select this second half as our final sampleof giants, and repeat this halving of the CMD process withthe real data in Fig. 1 (d).Should this method be applied to regions away from theGalactic Plane, where the line of sight extinction is lower andtherefore the distinction between the giant and dwarf starsis less apparent, it may be necessary to statistically separatethe two populations. However as there is a clear distinctionbetween populations for all regions studied in this paper,such a process is not required.Table 1 contains the number of sources that remain af-ter each cut. The Besan¸con data do not model stars with aninfrared excess. Such stars are abundant in star forming re-gions and are positioned to the right of the bulk of the data c (cid:13) , 1–18 Figure 1. a (Top left): A CCD of Besan¸con data modified as in Stead & Hoare (2009) to replicate the UKIDSS data centred on theRMS source G48.9897-00.2992 (see b). Stars that are redder than a G0III (red points) have been separated from the remaining datausing a CK04 G0III reddening track (black line). b (Top right): Same as (a) except using UKIDSS data centred on the RMS sourceG48.9897-00.2992, covering an area of 60 ′ x6 ′ . c (Bottom left): A CMD of the remaining Besan¸con data (red points in (a)). Dwarf andgiant stars are displayed as black and red points respectively and form two clumps of data. A black line has been placed approximatelyequidistant from each clump separating the CMD into two halves. Data to the right of the black line have been selected as the finalsample. The remaining red points are subgiants, bright giants and supergiants. d (Bottom right): A CMD of the remaining UKIDSS data(red points in (b)). Like in (c), a black line has split the CMD into two halves, data to the right of the black line have been selected asthe final sample. on a CCD, as such they are removed during the first datacut. In order to replicate the UKIDSS data, the Besan¸condata are clipped at the minimum and maximum J, H andK UKIDSS magnitudes. Of the final 1,339 synthetic stars,1,247, of a possible 1,626 from the total data set, are giants.Of the 1,247 giants in this final subset, 1,235 have a spectraltype of G0 or later. Therefore the reddest giants, spectraltype G0 or later, make up over 92% of the final UKIDSSsample.As shall be discussed in the following section, we dered-den the final UKIDSS subset to an intrinsic giant locus on aCCD, created using CK04 stellar models, in order to derivedistances to the molecular clouds they surround. As overhalf of the 1,247 giants in the final Besan¸con subset have aspectral type between K0 and K1, we use a K0III reddeningtrack to deredden the UKIDSS data. Using a K0III redden-ing track, created with the extinction law of Stead & Hoare (2009), we calculate an approximate extinction-colour rela-tionship, A V ∼ J isdetermined directly and converted to a value of A V usingthe ratio A J /A V =0.2833, calculated using the Cardelli et al.(1989) extinction curve with R V =3.1 (obtained from the Tri-legal website http://stev.oapd.inaf.it/cgi-bin/trilegal). It isnoted in the literature that the value R V =3.1 may not beappropriate for molecular clouds, however for the purposeof this paper it provides only a scaling between A K and A V and does not effect the errors of any derived results. To illustrate the dereddening process and how the presenceof molecular clouds along lines of sight can be detected, weobtain two samples of stars extracted from two different, c (cid:13) , 1–18 olecular cloud distance determination from deep NIR survey extinction measurements ′ x15 ′ areas of the sky. The first area has been centredon the RMS source G048.9897-0.2992 and therefore has amolecular cloud along the line of sight. The second area iscentred on the Galactic coordinates G048.9897-0.7000. Thearea was visually selected from a region in the GRS thatshowed no obvious signs of CO, and therefore the line ofsight extinction is likely to be free from dense molecularclouds.
The stars along each line of sight have been colour-colourand colour-magnitude selected, as described in the previoussection, to obtain a sample of stars primarily composed ofred giants. We use a CK04 K0III reddening track to dered-den each star in the sample created using the average ex-tinction power law of Stead & Hoare (2009). However to ac-count for the error created by dereddening stars of differingspectral types along a K0III reddening track, instead of red-dening tracks specific to the spectral type of each star, weincrease the error in the average extinction power law to α =2.14 +0 . − . . Each star is dereddened from its position on aCCD, along the K0III reddening track, to the point of inter-section on the giant locus. As the K0III reddening track hasbeen created by convolving the progressively redder spectraof a CK04 K0III stellar model through the UKIDSS filters,the length of the reddening track traversed directly relatesto the amount extinction each star suffers. The photometricerrors relate to the error in the point of intersection withthe giant locus, and therefore relate to the error in the de-termined extinction. V plots and A V histograms A distance-A V plot for the region G48.9897-0.2992, usingthe ∼ ′ x15 ′ tile that is centred spatially closest to the RMSsource. At ∼ V .The position of this rise is consistent with the presence of amolecular cloud at the RMS kinematic distance of 5.2 kpc.Stars can also be binned into small groups representingsmall increments of extinction to construct A V histograms.When plotting an A V histogram of the synthetic data cen-tred on the region G48.9897-0.2992, the sharp rise in extinc-tion in Fig. 2 (a), at ∼ V . In comparison, thesame synthetic data, reddened using a smooth extinctiondistribution model of 1.4 mag kpc − , produces a steady riseand fall in star counts of the over a similar range in theA V histogram (Fig. 2 (b)). If a distance-A V plot could beconstructed that contained precise distance and A V mea-surements for each star in the field of view then, assumingno stars are situated inside the molecular cloud, the molec-ular cloud would be represented by a vertical rise in theextinction distribution at the exact distance to the molecu-lar cloud. The corresponding A V histogram would containa sharp fall and rise in star counts, with a gap equivalent tothe total A V of the molecular cloud.Using only photometric data, it is possible to determine the amount of extinction a particular star suffers if accurateintrinsic colours are known. The amount of extinction suf-fered by a star is proportionate to how far the star moves,along a reddening track, on a colour-colour diagram (CCD),and can therefore be determined by dereddening individualstars along reddening tracks to their corresponding intrinsiccolours. In this case the colour selected giants are dered-dened to a giant locus. The giant locus has been generatedusing UKIDSS filter profiles and the CK04 stellar models(Stead & Hoare 2009). If we can accurately determine theamount of extinction suffered by every star along a partic-ular line of sight, then by creating A V histograms the pres-ence of a molecular cloud can be detected by the drop instar counts. Fig. 3 (a and b) contain A V histograms of realstars extracted from the two previously mentioned re-gions G048.9897-0.2992, centred on an RMS source, andG048.9897-0.7000, centred on a CO featureless region ofspace. As the A V histogram that is centred on an RMSsource will contain a molecular cloud along the line of sight,like the blue histogram in Fig. 2 (b), there are two distinctpeaks in the histogram, separated by a large dip in the sourcecounts. The second region, that does not contain a molec-ular cloud, produces an A V histogram with a steady riseand fall in star counts, and has a similar morphology to theblack histogram in Fig. 2 (b). As noted, the presence of amolecular cloud in the former histogram creates two distinctpeaks in the histogram. The far edge of the first peak there-fore represents the beginning of the molecular cloud. In thereverse manner, the near edge of the second peak thereforerepresents the end of the molecular cloud. To estimate thewidth of the gap, and therefore determine the A V of themolecular cloud, two skewed Gaussians are fit to each peak.The respective 1 σ deviations are used to define the edge ofeach peak, and therefore the difference between them is de-fined as the A V of the molecular cloud. In a similar fashionthe far line of sight extinction is defined as the 3 σ deviationto the far side of the second peak. In Fig. 2 (b), as thereis no molecular cloud and therefore no second peak, the 3 σ deviation is measured from a single skewed Gaussian.In this paper we have defined the far line of sight ex-tinction as the 3 σ deviation of all extinction measurements.This should be distinguished from the total line of sight ex-tinction, defined as the amount of extinction suffered alongthe line of sight towards the edge of the thin disk. Differencesbetween the far and total line of sight extinction measure-ments can occur for two reasons. First, there may be a largeamount of diffuse extinction behind the last detected cloudthat would not fit well to a skewed Gaussian distribution.More importantly however, it could be that along the line ofsight of the previously mentioned region G048.9897-0.7000,used to construct Fig. 3 (b), there could be a molecular cloudwith an optical depth large enough to prevent stars at thefar side of the cloud being detected. Therefore the measuredfar line of sight extinction, that is dependent upon the depthof the photometry used, would be very different to the totalline of sight extinction. However, the good agreement be-tween real data and synthetic data (see section 5.2, Fig. 8)suggests that the far and total line of sight extinction are c (cid:13) , 1–18 Figure 2. a (Left): A distance-A V plot containing synthetic data showing the extinction distribution model (blue line) created toreproduce the M06 data (red error bars) centred spatially closest to the RMS source G048.9897-0.2992. The black line represents thesmooth extinction distribution model of 1.4mag kpc − . b (Right): A synthetic A V histogram of each extinction distribution presentedin the distance-A V plot (Left panel). The blue data have a drop in star counts between A V ∼ ∼
13, corresponding to the suddenincrease in extinction beginning at ∼ V plot. Figure 3. a (Left): An A V histogram of real stars extracted from a 15 ′ x15 ′ region centred on the RMS source G048.9897-0.2992. Wehave defined the total line of sight extinction to the far side of the molecular cloud, as the 1 σ width (dashed blue line) on the left sideof the skewed Gaussian (red line). (Right): An A V histogram of a 15 ′ x15 ′ region centred on an unremarkable region of space (see text)at G048.9897-0.7000. The histogram shows no presence of a molecular cloud. We define the far line of sight extinction (see text) as the3 σ deviation of all extinction measurements (dashed green line) of the fitted skewed Gaussian (red line). often the same.It is possible to repeat both of these processes in smallincrements for large fields to produce two different types ofextinction map, far line of sight extinction (FLSX) maps andmolecular cloud extinction (MCX) maps. The latter can becreated by plotting A V histograms and identifying which re-gions show the presence of molecular clouds. The A V of eachcloud can be measured and used to construct an extinctionmap, showing both the location and size of any clouds in thefield of view. In comparison Lombardi (2009), by measuringthe colour excess of background stars, evaluate the extinc-tion at any location in the sky using a weighted average ofextinction measurements to stars that are angularly close toa given location on the map.Using the above processes, both types of extinctionmaps have been created for a 2 o x2 o region centred at G49.5+0.0, containing the RMS source G048.9897-0.2992(The region was not centred closer to the RMS source dueto incomplete UKIDSS data at l < V histograms for6 ′ x6 ′ tiles that are therefore over 6 times the resolution ofthe 15 ′ x15 ′ M06 distributions. For each histogram we mea-sure the far line of sight extinction, and depending whetheror not the histogram contains the presence of a molecularcloud, the A V of the cloud is determined. Some histogramsshow the possible presence of more than one molecular cloudalong the line of sight. In such cases we determine the farline of sight extinction to the far side of the most prominentmolecular cloud. We analyse one 6 ′ x6 ′ region of sky and thenmicrostep by shifting the field of view by 3 ′ , repeating theprocess for the entire 2 o x2 o region. The large region is thenagain split into 6 ′ x6 ′ tiles, however the extinction associated c (cid:13)000
13, corresponding to the suddenincrease in extinction beginning at ∼ V plot. Figure 3. a (Left): An A V histogram of real stars extracted from a 15 ′ x15 ′ region centred on the RMS source G048.9897-0.2992. Wehave defined the total line of sight extinction to the far side of the molecular cloud, as the 1 σ width (dashed blue line) on the left sideof the skewed Gaussian (red line). (Right): An A V histogram of a 15 ′ x15 ′ region centred on an unremarkable region of space (see text)at G048.9897-0.7000. The histogram shows no presence of a molecular cloud. We define the far line of sight extinction (see text) as the3 σ deviation of all extinction measurements (dashed green line) of the fitted skewed Gaussian (red line). often the same.It is possible to repeat both of these processes in smallincrements for large fields to produce two different types ofextinction map, far line of sight extinction (FLSX) maps andmolecular cloud extinction (MCX) maps. The latter can becreated by plotting A V histograms and identifying which re-gions show the presence of molecular clouds. The A V of eachcloud can be measured and used to construct an extinctionmap, showing both the location and size of any clouds in thefield of view. In comparison Lombardi (2009), by measuringthe colour excess of background stars, evaluate the extinc-tion at any location in the sky using a weighted average ofextinction measurements to stars that are angularly close toa given location on the map.Using the above processes, both types of extinctionmaps have been created for a 2 o x2 o region centred at G49.5+0.0, containing the RMS source G048.9897-0.2992(The region was not centred closer to the RMS source dueto incomplete UKIDSS data at l < V histograms for6 ′ x6 ′ tiles that are therefore over 6 times the resolution ofthe 15 ′ x15 ′ M06 distributions. For each histogram we mea-sure the far line of sight extinction, and depending whetheror not the histogram contains the presence of a molecularcloud, the A V of the cloud is determined. Some histogramsshow the possible presence of more than one molecular cloudalong the line of sight. In such cases we determine the farline of sight extinction to the far side of the most prominentmolecular cloud. We analyse one 6 ′ x6 ′ region of sky and thenmicrostep by shifting the field of view by 3 ′ , repeating theprocess for the entire 2 o x2 o region. The large region is thenagain split into 6 ′ x6 ′ tiles, however the extinction associated c (cid:13)000 , 1–18 olecular cloud distance determination from deep NIR survey extinction measurements Figure 4. a (Top): A FLSX map from the 2 o x2 o region centred at G49.5+0.0. The 15, 18, 21 and 24 A V levels are plotted in variousshades of red. Blue contour lines represent the 11 A V level. The RMS source is plotted as a red triangle. Blue + symbols representregions where the extinction was too high to accurately determine the far line of sight extinction. The region of sky used to determinethe M06 data is plotted as a dashed rectangle. A 9 ′ x6 ′ region surrounding the RMS source is plotted as a solid rectangle. b (Bottom):The same contour lines from (a) have been overlaid with a GRS integrated intensity image from the same region, created using the fullvelocity range available, from -5 to 85 km s − .c (cid:13) , 1–18 Figure 5. a (Top): A MCX map from the 2 o x2 o region centred at G49.5+0.0. The 4, 6, 8 and 10 A V levels are plotted in various shadesof red. The RMS source is plotted as a red triangle. Blue + symbols represent regions where the extinction was too high to accuratelydetermine the A V of detected clouds. The region of sky used to determine the M06 data is plotted as a dashed rectangle. A 9 ′ x6 ′ regionsurrounding the RMS source is plotted as a solid rectangle. b (Bottom): The same contour lines from (a) have been overlaid with a GRSintegrated intensity image from the same region, created using a velocity range from 60 to 75 km s − . c (cid:13) , 1–18 olecular cloud distance determination from deep NIR survey extinction measurements to each tile is taken from an average of the four surround-ing microstepped 6 ′ x6 ′ tiles. This process does not improvethe resolution of the final extinction map, however it doessmooth the extinction map, averaging out any anomalousA V measurements.Fig. 4 a contains a FLSX map from the 2 o x2 o regioncentred at G49.5+0.0. Contour lines show the 11, 15, 18,21 and 24 A V levels. The RMS source G048.9897-0.2992(red triangle) is contained within the 21 A V level. Fig. 4(b) contains the same extinction plot overlaid with a GRSintegrated intensity image, from the same region, in orderto draw a comparison between the positions of molecularclouds and the regions of high extinction traced out by thecontours. The GRS image has been created using the fullvelocity range available from -5 to 85 km s − . The contourlines have mapped out the bulk of the extinction shown inthe GRS data, and from this we can estimate the extent ofthe molecular cloud that contains the RMS source. Thereare two other regions surrounded by A V =21 contour lines,at ∼ G48.8+0.1 and ∼ G50.4-0.4, in both cases there do ap-pear to be other large groups of molecular clouds at thesepositions.Fig. 5 a contains a MCX map from the 2 o x2 o region cen-tred at G49.5+0.0. Contour lines show the 4, 6, 8 and 10 A V levels of the measured depth of the molecular clouds. TheRMS source G048.9897-0.7000 (red triangle) is containedwithin the 8 A V level. Fig. 5 (b) contains the same extinc-tion plot overlaid with the same GRS integrated intensityimage, plotted in Fig. 4 (b), however only the velocity range60 to 75 km s − has been considered. This range correspondsto the approximate 3 σ width of the measured kinematic ve-locity of the molecular cloud associated with the RMS source(Urquhart et al. 2008). Like in Fig. 4 (b) the contour lineshave mapped out the bulk of the extinction shown in theGRS data, and as before we can estimate the extent of themolecular cloud that contains the RMS source. Both typesof extinction maps show very similar features, however in theMCX map, large areas are featureless due to the absence ofmolecular clouds. In all plots a 9 ′ x6 ′ region surrounding theRMS source has been overlaid. Stars within this region havebeen selected to further analyse in the following section. V relationship Fig. 6 contains an A V histogram of real stars extracted fromaround the previously mentioned 9 ′ x6 ′ region surroundingthe RMS source G048.9897-0.2992. The morphology of theA V histogram is similar to the synthetic A V histogram, cre-ated using the EDM relating to the M06 data, presented inFig. 2 (b - blue histogram). As both histograms are similarit indicates that the M06 data are an accurate representa-tion of the extinction distribution along this particular lineof sight. However there is an important feature worth not-ing, at A V ∼
12 there is a drop in source counts creating agap in the histogram, occurring due to the presence of themolecular cloud along the line of sight. If we estimate therange of A V along the histogram that the cloud covers, andwe have an accurate line of sight specific extinction-distance Figure 6.
An A V histogram of real stars from a 9 ′ x6 ′ regioncentred on the RMS source G048.9897-0.2992. The near and farsides of the molecular clouds are marked with dashed blue lines,derived from the 1 σ deviations of the Gaussians (solid blue lines)fitted to the red bins. relationship, then it is possible to determine the distanceto the cloud. The distance and the error in the distance tothe cloud are derived by first measuring the A V values repre-senting the beginning and end of the molecular cloud. TheseA V measurements are then converted to distances using theextinction-distance relationships provided by the M06 data.The distance to the cloud is determined as the average ofthese two measurements, and the error, the difference be-tween them. The M06 error bars in A V are also consideredand from this, we estimate the distance to the RMS sourceto be D = 5.5 ± ± V histogram above the noise, a goodness offit statistic is calculated as the square root of the summedsquared residuals, presented in the following equation: β = P ni =1 ( O i − E i ) n , (1)where O i is the actual star count and E i is the expected starcount, and n is the number of bins in the histogram. Thegoodness of fit statistic is calculated for both Gaussians, fit-ted to each peak in the histogram. A single Gaussian is thenfitted to the same, combined range of data across both pre-vious peaks. A larger goodness of fit statistic is determinedwhen fitting one Gaussian, thereby suggesting a poorer fit,than when using of two Gaussians. V gap In order to test the reliability of using two Gaussians tomeasure the A V of a molecular cloud on an A V histogram,we have measured the dip in source counts in 2500 differentsynthetic A V histograms. Each synthetic histogram has beencreated using a smooth EDM (EDM1) of 1.5 mag kpc − andcontains a cloud with A V =1.5 at 5.2 kpc. To model the ef-fect of cloud patchiness, we also combine a smooth EDM(EDM2) of 1.5 mag kpc − without a synthetic cloud alongthe line of sight. The ratio of EDM2 to EDM 1 is allowed c (cid:13) , 1–18 Figure 7.
An A V histogram of synthetic stars has been used totest the reliability of using two Gaussians to measure the A V ofa molecular cloud (see text). Each skewed Gaussian is shown asa red line and the corresponding 1 σ widths are shown as bluedashed lines. to vary between 0% and 40%. Larger ratios than 40% makeit difficult to detect the synthetic cloud above the noise inthe histogram. Realistic errors are given to the syntheticdata, and from these 2500 measurements, we compute thegap to be A V =1.6 ± V yields a distanceto the RMS source G048.9897-0.2992 of D = 5.6 ± ± ∼ ∼ − . Therefore large increases in the error in A V willonly translate into small errors in the derived distance. To-wards regions where the extinction-distance relationship isshallower, the additional error in the gap measurement willtranslate into larger errors in the derived distance. All sub-sequent distances derived in this paper include the error inthe extinction-distance relationship, and the ± V gap at A V ∼
12, the A V histogram begins to show a reduc-tion in star counts at A V ∼
8, continuing until A V ∼
12. It ispossible, due to the low number statistics, that this largerrange is entirely caused by the molecular cloud and shouldbe the measured dip. The distance assigned to this dip isD = 5.1 ± V , this is due tothe steep slope on the EDM reducing the range of possibledistances. However, we do not believe that the molecularcloud is responsible for this broader A V gap. There are sev-eral molecular clouds, identified in the Galactic Ring Survey,within the vicinity of the molecular cloud that contains the Figure 8.
An A V histogram of real stars (red histogram) takenfrom the same region of sky that was used to create the Marshalldata (see text). The synthetic histogram, containing the samenumber of sources as the real histogram, is presented in black. RMS source. The majority of these clouds are at a similarkinematic distance to G048.9897-0.2992 and so may be re-sponsible for the broadening of the A V gap. As the M06 dataare not centred on the RMS source, the molecular cloud con-taining the RMS source is unlikely to be entirely responsiblefor the extinction measurements, along the line of sight, usedto create the M06 data.The particular M06 data set used to model the ex-tinction along the line of sight extinction towards theRMS source G048.9897-0.2992, is centred on the coordi-nates G049.00-00.25 and obtained from a 15 ′ x15 ′ region. Wehave dereddened sources extracted from the same 15 ′ x15 ′ re-gion as the M06 data and compared, in Fig. 8, a real A V histogram with a synthetic A V histogram. The synthetichistogram has been created by taking a random sample ofBesan¸con data equal to the number of real stars. Both his-tograms show a similar morphology, however the real his-togram no longer has a second deep dip at A V ∼
12. It isonly when we extract stars from a smaller region centredexactly on the molecular cloud that this drop appears. Thissuggests that the A V dip in Fig. 6 is entirely due to themolecular cloud centred on the RMS source, and as such,the distance to the RMS source is, D = 5.6 ± V histogram in Fig. 8 was constructedwith synthetic stars as distant as 15 kpc. As the real A V histogram also covers a similar range of A V as the syntheticA V histogram, it can be considered that for this particularline of sight, the far line of sight extinction and the totalline of sight extinction, previously discussed in section 4.3,are the same. As previously mentioned, Urquhart et al (in prep.)have identified the molecular clouds from Rathborne et al.(2009) that are associated with 292 RMS sources. AsRathborne et al. (2009) have listed the Galactic position andthe longitudinal and latitudinal FWHM of each cloud, thisinformation can be used in the same manner as discussedto derive distances, independent to kinematic methods, to c (cid:13)000
12. It isonly when we extract stars from a smaller region centredexactly on the molecular cloud that this drop appears. Thissuggests that the A V dip in Fig. 6 is entirely due to themolecular cloud centred on the RMS source, and as such,the distance to the RMS source is, D = 5.6 ± V histogram in Fig. 8 was constructedwith synthetic stars as distant as 15 kpc. As the real A V histogram also covers a similar range of A V as the syntheticA V histogram, it can be considered that for this particularline of sight, the far line of sight extinction and the totalline of sight extinction, previously discussed in section 4.3,are the same. As previously mentioned, Urquhart et al (in prep.)have identified the molecular clouds from Rathborne et al.(2009) that are associated with 292 RMS sources. AsRathborne et al. (2009) have listed the Galactic position andthe longitudinal and latitudinal FWHM of each cloud, thisinformation can be used in the same manner as discussedto derive distances, independent to kinematic methods, to c (cid:13)000 , 1–18 olecular cloud distance determination from deep NIR survey extinction measurements RMS sources. The FWHM measurement of each cloud canbe used to ensure we are observing stars directly in frontand behind each cloud analysed.From the 292 RMS-GRS associations identified byUrqhart et al (in prep.), 173 have available J, H and KUKIDSS GPS data. To detect the presence of a molecularcloud in an A V histogram, enough foreground giant starsmust be observed to notice the reduction in star counts perA V bin that signals the presence of a molecular cloud. There-fore there will be a lower limit to the derivable distances tomolecular clouds. If 3 star counts per A V bin are needed todetect the presence of the foreground giants, in the synthetichistogram in Fig. 8 the first A V bin containing this numberof sources occurs when A V ∼ V plotin Fig. 2, created with the M06 data, converts this A V valueinto a distance of ∼ ◦ of the Galactic Centre toavoid the long thin Galactic bar, since this is not included inthe Besan¸con model data. As the RMS and GRS kinematicdistances have been derived using different Galactic rota-tion models, there are certain sources that do not possessan RMS kinematic ambiguity but are flagged as having soin the GRS catalogue. These clouds have also been excludedreducing our sample size to 74. It is not possible to assignan upper limit to the derivable distances, as the cut-off willbe dependent upon the total extinction suffered and there-fore photometric depth. Clouds at higher Galactic latitudesmay suffer less extinction than those at lower latitudes andit will therefore be possible to ’see further’ along these linesof sight. We have assigned an initial upper limit of 9 kpc,and due to this upper limit, we have 34 clouds in our finalsample that have a near distance larger than 2 kpc and afar distance smaller than 9 kpc.When using the GRS FWHM measurement to identifystars along the same line of sight as a molecular cloud, thearea observed is very important. A large star count is neededto detect the presence of the cloud in an A V histogram, how-ever, assuming each cloud to possess a spherical shape, starsalong the line of sight of the edge of the cloud will suffer lessextinction than those along the line of sight of the centre.Furthermore, the larger the area the greater the chance ofcontamination from overlapping clouds. To avoid excessivenoise in the resultant A V histogram we need to limit thesize of the area observed, yet keep it large enough to detectenough stars. The size of each region observed is done on acloud-by-cloud basis and we typically observe between a 0.6and 1.0 σ width of the cloud. Finally, an EDM is createdusing the M06 data set that is spatially closest to the centreof the molecular cloud. The previous region surrounding the RMS sourceG048.9897-0.2992 is particularly simple to analyse fortwo reasons. First, from inspection of the M06 data, thereappears to be only one, very sharp rise in extinction. Forthis reason the distance to the cloud, using Fig. 2 (a),can be visually estimated to be 5.0 ± ± ± V plot of the extinctiondistribution model used to reproduce the M06 data assignedto the cloud. Unlike Fig. 2 (a), Fig. 9 (a) does not containa sudden jump in extinction at the position of any of thekinematic distances. Therefore the resolution of the M06data is too low to distinguish between the near and farRMS kinematic distances. However, the M06 data stillprovide a reliable description of how the extinction relatesto distance along the line of sight.Fig. 9 (b) contains an A V histogram of the dereddenedgiants extracted from a 1 σ region of the molecular cloud.The histogram has two clear dips in star counts at A V ∼ V ∼
11 that each separate two distinct peaks. We usethe extinction distribution to plot the kinematic distanceson the A V histogram. The RMS and GRS kinematicdistances are plotted as green and red arrows respectively.We first measure the dip that appears to be associatedwith the kinematic distances, and determine the distanceto be D = 6.9 ± V ∼ ± σ level, there still remains some level of ambiguity tothe derived distance to this molecular cloud. However, uponspatial examination of the entire GRS catalogue, it appearsthe region of sky previously studied also overlaps with asecond molecular cloud G041.04-0.26, with a GRS distanceD = 4.7 kpc. As the RMS source is spatially nearer theGRS cloud G041.04-0.66, the assigned distance to the RMSsource is D = 6.9 ± The final 34 molecular clouds have each been sorted into oneof three groups depending upon the features present in the c (cid:13) , 1–18 Figure 9. a (Left): A distance-A V plot containing the extinction distribution model (black line) created to reproduce the M06 data (blueerror bars) along the line of sight of the GRS molecular cloud G041.04-0.66. The GRS and two RMS kinematic distances are plotted asred and green arrows respectively. b (Right): An A V histogram of real stars from a small region centred on the GRS molecular cloudG041.04-0.66 contains a dip in star counts at A V ∼
11. Two Gaussians have been fitted to each peak separated by the dip. The 1 σ widthshave been used to determine the distance to the molecular cloud. Table 2.
Clouds where sufficient data are present to examine near and far distances.GRS Cloud Near Far GRS D error(kpc) (kpc) (kpc) (kpc)(1) (2) (3) (4) (5) (6)GRSMC G031.39+0.29 6.35 8.16 6.55 6.6 0.5GRSMC G032.09+0.09 6.13 8.29 7.07 7.2 1.1GRSMC G039.34–0.31 4.55 8.59 4.55 5.3 0.7GRSMC G040.34–0.26 5.34 7.63 5.43 4.5 0.8GRSMC G042.14–0.61 4.99 7.62 5.12 4.3 0.5GRSMC G042.44–0.26 4.87 7.68 4.90 5.1 0.7GRSMC G043.34–0.36 4.46 7.91 4.65 4.1 0.7GRSMC G045.14+0.14 4.53 7.48 4.53 4.4 0.6GRSMC G050.24–0.61 3.22 7.66 3.20 3.2 0.2GRSMC G050.84+0.24 3.43 7.32 3.53 4.5 0.4GRSMC G052.79–0.56 4.78 5.47 5.78 5.3 0.6GRSMC G054.14–0.06 3.76 6.21 6.32 7.0 1.0GRSMC G054.39–0.46 2.76 7.20 6.82 6.8 0.8GRSMC G029.89–0.06 6.14 8.60 6.78 6.5 0.7GRSMC G030.29–0.21 6.76 7.90 7.32 7.2 0.7GRSMC G031.04+0.29 6.16 8.44 6.65 6.3 0.8GRSMC G033.04+0.04 5.30 8.96 8.73 8.1 0.9GRSMC G041.04–0.66 5.78 7.04 6.38 6.9 0.5GRSMC G043.89–0.81 3.92 8.33 3.85 4.4 0.6GRSMC G052.79+0.29 4.55 5.70 6.10 6.9 1.1 subsequent A V histograms. For each of the final 34 clouds wehave created both a distance-A V plot, containing the M06data and an extinction distribution model (EDM), and anA V histogram.The first group contains 20 clouds and the correspond-ing A V histogram of each has a strong presence of one ormore molecular clouds. We derive the distances of thesemolecular clouds in an attempt to distinguish between thenear and far kinematic distances. Results are presented inTable 2 and the table is split into two subgroups. The firstsubgroup contains regions where only one obvious molecu-lar cloud is present in the A V histogram, such as the cloudcontaining G048.9897-0.2992 (Fig. 6). The second subgroup contains regions where multiple molecular clouds are presentin the A V histogram, such as the cloud G041.04-0.664 (Fig.9b). In cases where there are multiple molecular clouds, weuse the cloud that appears to be associated with either thenear or far distance, and address the presence of the ad-ditional clouds in the Appendix by looking for overlappingclouds in the GRS. The columns of Table 2 are as follows:(1) the molecular cloud name; (2) the near RMS distance;(3) the far RMS distance; (4) the GRS distance; (5) and (6)the distance and error derived in this paper.The second group contains 10 clouds and the corre-sponding A V histograms do not contain an adequate numberof sources with large enough values of A V to exclude the far c (cid:13) , 1–18 olecular cloud distance determination from deep NIR survey extinction measurements Figure 10. a: A distance-A V plot containing the extinction distribution model (black line) created to reproduce the M06 data (blueerror bars) along the line of sight of the GRS molecular cloud G042.04-0.01. The GRS and two RMS kinematic distances are plotted asred and green arrows respectively. b: An A V histogram of real stars from a small region centred on the cloud G042.04-0.01. As data areinsufficient to exclude the far kinematic distance, but there is also no obvious cloud at the near distance, the cloud has been placed inthe first subset of Group 2 (see text). c: Same as (a) for the cloud G049.39-0.26. d: Same as (b) for the cloud G049.39-0.26 except thedata are insufficient to exclude both the near and far kinematic distances. For this reason the cloud has been placed in the second subsetof Group 2. e: Same as (a) for the cloud G043.3900-0.66. f: Same as (b) for the cloud G043.39-0.66, except no obvious clouds are presentin the A V histogram and so the cloud has been placed in Group 3. kinematic distance. Results are presented in Table 3 and thetable is split into two subgroups. In some cases it is still pos-sible to exclude the near distance due to the apparent lack ofa molecular cloud at the near distance. The first and secondsubgroups contain regions where we have and have not been able to exclude the near kinematic distance respectively, Fig.10 (b) gives an example of an A V histogram where data areinsufficient to exclude the far kinematic distance, but alsocontains no obvious cloud at the near distance, thereby solv-ing the near/far ambiguity through exclusion. Fig. 10 (d) c (cid:13) , 1–18 Table 3.
Clouds where data are insufficient to exclude far distances.GRS Cloud Near Far GRS Exclude Near?(kpc) (kpc) (kpc)(1) (2) (3) (4) (5)GRSMC G030.44–0.26 6.62 8.04 7.30 YGRSMC G041.34+0.09 4.12 8.64 8.55 YGRSMC G042.04–0.01 3.87 8.74 8.60 YGRSMC G043.19–0.51 4.15 8.24 8.27 YGRSMC G044.29+0.04 4.33 7.83 8.02 YGRSMC G044.34–0.21 5.33 6.90 6.80 YGRSMC G045.49+0.04 4.71 7.22 7.45 YGRSMC G028.59+0.04 6.16 8.76 6.60 NGRSMC G037.69+0.09 6.18 7.20 6.70 NGRSMC G049.39–0.26 4.99 6.04 6.82 N
Table 4.
Clouds where data are insufficient to detect the presence of a molecular cloud.GRS Cloud Near Far GRS(kpc) (kpc) (kpc)(1) (2) (3) (4)GRSMC G032.99+0.59 5.91 8.36 8.05GRSMC G030.79–0.06 5.77 8.84 6.22GRSMC G043.39–0.66 4.32 8.01 8.18GRSMC G043.49–0.71 3.32 8.95 2.83 gives an example of an A V histogram where data are insuf-ficient to exclude both the near and far kinematic distances.The columns of Table 3 are the same Table 2 except as fol-lows; (5) a flag denoting if the near kinematic distance canbe excluded.The third group contains 4 clouds and the correspond-ing A V histograms do not show the significant presence of amolecular cloud at either the near or far kinematic distance.Results are presented in Table 4. The columns of Table 4are the same Table 2. Roman-Duval et al. (2009) providethe CO luminosity (K km s − pc ) of each cloud in theGRS which can be used to estimate the A V of each cloud.This is done as follows; an average CO luminosity of eachcloud is determined by estimating the area of each fromthe Galactic longitudinal and latitudinal FWHM and theGRS distance. This value is then converted to a CO col-umn clump density, in cm − , using the equation N( CO) =8.75 x 10 W( CO), from Simon et al. (2001). Finally thisvalue is converted to A V using the equation A V = 4.24 x10 − N( CO) + 1.67 from Goodman et al. (2009). We donot expect this computed value of A V to agree particularlywell with the value of A V , used to determine the distanceto the cloud, measured in each histogram. This is becausethe computed value of A V has been averaged over the en-tire molecular cloud and the resolution of the GRS data ismany times greater than the approximate, 6 ′ x6 ′ tiles usedto construct each A V histogram. Furthermore, the spatialsubstructure of each cloud has not been considered.Three of the clouds in group 3 have the three lowest A V values, derived from the CO luminosities, in our sample of34 clouds. This provides a likely explanation as to why themolecular clouds could not be detected above the noise inthe A V histograms. For the remaining cloud, G30.79-0.06, the reverse is true. G30.79-0.06 has one of the largest A V values, derived from the CO luminosities, out of the sam-ple of 34 clouds. Despite this however, it failed the goodnessof fit test as the line of sight extinction is too large, fromthe combination of both the cloud G30.79-0.06 and a secondmolecular cloud, as shall be discussed in the Appendix, todetect an adequate amount of stars at the near side of thecloud. Fig. 10 (f) contains an example A V histogram fromgroup three. Distance-A V plots and A V histograms for theremaining regions, from all three groups, are available withthe online material.To draw a comparison between our results and both theRMS and GRS kinematic distances, Fig. 11 contains a plotof the GRS distances, both RMS distances and the distancesderived to each of the 20 clouds in Group 1, subtracted fromthe GRS distance. The grey line crossing the origin there-fore represents the GRS distance subtracted from itself. Theopen blue circles represent the near RMS distance and theclosed blue circles represent the far RMS distance. The rederror bars represent the 20 distances derived in this paperfrom group 1.The near/far distance ambiguity has been resolved for27 clouds out of the sample of 34 molecular clouds. Distanceshave been derived to 20 clouds that are independent to kine-matic methods. Of the 20 distances derived, 19 agree theGRS distance to within the 2 σ level, and 18 of the 20 agree towithin the 1 σ level, however this does not take into accountthe error on the GRS distance. One cloud, G050.84+0.24with a GRS distance D = 3.5 kpc and a distance derivedin this paper D = 4.5 ± σ level.There is a second overlapping cloud with a GRS distance of5.3 kpc, however there is no obvious sign of a second molec-ular cloud in the A V histogram, furthermore the distance c (cid:13) , 1–18 olecular cloud distance determination from deep NIR survey extinction measurements Figure 11.
For the 20 molecular clouds in Group 1, the GRS distances, both RMS distances and the distances derived to each cloudin this paper have been subtracted from the GRS distance. The grey line crossing the origin therefore represents the GRS distancesubtracted from itself. The open blue circles represent the near RMS distance and the closed blue circles represent the far RMS distance.The red error bars represent the distances derived in this paper. derived in this paper correctly resolves the near/far ambi-guity.In many cases the GRS distance agrees within errorswith one of the RMS kinematic distances. However, as dis-cussed previously, due to the difference in choice of theGalactic rotation models used to derive both the RMS andGRS kinematic distances, there are some differences be-tween the two sets of kinematic distances. Error bars for theGRS distances have not been plotted as Roman-Duval et al.(2009) do not include specific errors in each measurement,however they will be very similar to the size of the errorbars on the RMS distances. Taking this into account, alldistances measured in this paper agree well with the GRSresolved kinematic distances.There are often large differences between kinematicdistances and those derived by independent means. Forexample, there are differences of ∼ ∼ ∼ Of the 34 molecular clouds studied in this paper, we havedirectly resolved the near/far kinematic distance ambiguityfor 20 clouds by deriving a distance to each cloud. Thesedistances have been derived using near-infrared photometryand an existing line of sight specific extinction-distance re-lationship. Therefore the distances presented in this paperare independent to kinematic methods typically used to de-termine distances to molecular clouds. These distances havebeen used to resolve the kinematic distance ambiguity asso-ciated with each cloud, and from comparison to the work ofRoman-Duval et al. (2009), all 20 clouds have been resolvedcorrectly.For the remaining 14 clouds that we were unable toderive a distance to, 3 of the clouds were too optically shal-low to detect above the noise in subsequent A V histograms.One cloud had several high extinction clouds along the sameline of sight and so, due to a lack of foreground stars, wewere unable to constrain a distance to the cloud. Finally,the method failed for 10 clouds as the extinction along theline of sight was too large to detect stars at, and beyond,the far distance. However, for 7 of these 10 clouds, we couldnot detect the presence of a molecular cloud at the near dis- c (cid:13) , 1–18 tance, thereby solving the near/far ambiguity through ex-clusion. In all 7 occurrences our results agreed with thoseof Roman-Duval et al. (2009). In total, 27 clouds had theirnear/far ambiguity resolved.Although it was not possible to observe stars beyond thefar RMS kinematic distance assigned to 10 of the 34 molec-ular clouds, it may still be possible to extend our sample toinclude clouds further than the original 9 kpc cut applied.The majority of derived distances are below 7.5 kpc, how-ever the method fails when the extinction along the line ofsight is too large to detect stars at, and beyond, the far dis-tance. For this reason the method failed on some clouds, asclose as 6.6 kpc, and succeeded on others as far away as 8.7kpc. Success of the method depends on the total extinctionalong the line of sight. Although UKIDSS GPS data wouldallow the detection of stars suffering up to A V ∼
25 using theerror cuts detailed in this paper, from inspection of the A V histograms presented in this paper we can determine dis-tances to clouds that suffer below A V ∼
18 along the line ofsight, including the visual extinction of the cloud itself. Itmay be possible to increase the depth by relaxing the errorcut in the J band, the photometric band that suffers fromthe effect of extinction the most, without contaminating theresultant A V histograms significantly. Furthermore, for re-gions where the extinction along the line of sight exceeds 18magnitudes of visual extinction, it may still be possible toconfidently exclude the near distance.In this paper the GRS data provide a way to obtain theGalactic location and spatial extent of each molecular cloudstudied. However the GRS only covers a Galactic longituderange from l=18 o and l=55.7 o , between | b | < o . To extendthe work in this paper to regions outside of this range, molec-ular cloud extinction maps (section 4.3) could be used toidentify molecular clouds and measure their spatial extent.This process would work best at larger Galactic longitudeswhere the average line of sight extinction is typically lower,making it easier to detect the presence of molecular cloudsabove the background extinction level. We will be able toextend and improve the method to clouds in the southernhemisphere when the deeper VISTA data become available(Minniti et al. 2009). ACKNOWLEDGEMENTS
We thank the anonymous referee for suggestions that im-proved the results of this paper. This work is based in part ondata obtained as part of the UKIRT Infrared Deep Sky Sur-vey. This publication makes use of data products from theTwo Micron All Sky Survey, which is a joint project of theUniversity of Massachusetts and the Infrared Processing andAnalysis Centre/California Institute of Technology, fundedby the National Aeronautics and Space Administrationand the National Science Foundation. We made use of theVizieR service (http://vizier.u-strasbg.fr/viz-bin/VizieR) toobtain 2MASS data and the M06 extinction distributions.This publication makes use of molecular line data from theBoston University-FCRAO Galactic Ring Survey (GRS).The GRS is a joint project of Boston University and FiveCollege Radio Astronomy Observatory, funded by the Na-tional Science Foundation under grants AST-9800334, AST-0098562, and AST-0100793.
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Distance-A V plots and A V histograms for all the remain-ing regions are available with the online material in FiguresA1 to A8. In all cases the distance-A V plots contain theextinction distribution model (black line) created to repro-duce the M06 data (blue error bars) along the line of sightof each GRS cloud. The GRS and two RMS kinematic dis-tances are plotted as red and green arrows respectively. TheA V histograms contain the same red and green arrows cor-responding to the GRS and both RMS kinematic distances.In cases where a molecular cloud was present in the A V his-togram, the two Gaussians used to estimate the extinctionof, and from that the distance to, each cloud are shown asblue curves. The 1 σ width of each skewed Gaussian has beenindicated with blue dashed lines. A1 G029.89-0.06
The molecular cloud G029.89-0.06 has RMS distances of6.1/8.6 kpc and a GRS distance of 6.8 kpc. The distancederived in this paper is D = 6.5 ± V ∼
12. The deriveddistance to this second cloud is D = 8.3 ± σ level and so acertain level of ambiguity remains.The extracted region overlaps with a second molecularcloud G029.79-0.21. This second cloud, G029.89-00.26, hasa high CO luminosity and a GRS distance of 8.45 kpc,therefore providing a likely explanation for the presence ofthe second cloud.
A2 G030.29-0.21
The A V histogram, created from data extracted from aroundthe molecular cloud, G030.29-0.21, appears to contain twoA V dips of similar size (Fig. A1). Measuring the size of thesecond dip, situated at A V ∼
7, reveals a distance of D =4.6 ± V histogram has been accounted for. A3 G031.04+0.29
The molecular cloud G031.04+0.29 has RMS distances of6.2/8.4 kpc and a GRS distance of 6.7 kpc. The distancederived in this paper is D = 6.3 ± V ∼
9. The deriveddistance to this second cloud is D = 7.5 ± CO luminosities provid-ing a possible explanation for the presence of a second cloud.
A4 G033.04+0.04
The molecular cloud G033.04+0.04 has RMS distances of5.3/9.0 kpc and a GRS distance of 8.7 kpc. The distancederived in this paper is D = 8.1 ± V histogram, at A V ∼ ± σ level. There are four other molecu-lar clouds nearby, all with GRS distances of 7.1 kpc, whichcould account for the presence of a second molecular cloudin the A V histogram. A5 G043.89-0.81
The molecular cloud G043.89-0.81 has RMS distances of3.9/8.3 kpc and a GRS distance of 3.9 kpc. The distancederived in this paper is D = 4.4 ± V ∼
9. The deriveddistance to this second cloud is D = 5.3 ± A6 G052.79+0.29
The molecular cloud, G052.79+0.29, has RMS distances of4.6/5.7 kpc and a GRS distance of 6.1 kpc. The distancederived in this paper is D = 6.9 ± V ∼
12. The deriveddistance to this second cloud is D = 5.4 ± A7 G028.59+0.04
The molecular cloud G028.59+0.04 has RMS distances of6.2/8.8 kpc and a GRS distance of 6.6 kpc. The A V his-togram does not contain an adequate amount of data todetect a molecular cloud at the far RMS distance and soit has therefore been placed in group 2. There is however avery large dip in source counts in the A V histogram betweenA V ∼ ∼
14 (Fig. A1). The distance assigned to this dipis D = 5.3 ± V , however upon in-spection of the EDM there is a very large increase in A V beginning at ∼ σ level, there are severalother overlapping clouds covering a range of distances from ∼ ∼ A8 G045.49+0.04
G045.49+0.04 has been placed in group two as it is notpossible to exclude the far RMS distance (Fig. A6). It has c (cid:13) , 1–18 RMS distances of 4.7/7.2 kpc and a GRS distance of 7.5kpc. There is however evidence of a molecular cloud in theA V histogram at A V ∼
6. It has an assigned distance of D =4.6 ± V histogram, and so it may actually be possible toexclude the near distance. A9 G030.79-0.06
The molecular cloud G030.79-0.06 has RMS distances of5.8/8.8 kpc and a GRS distance of 6.2 kpc. It has failedthe goodness of fit test and so has been placed in group 3.There is however a very strong presence of a molecular cloudin the A V histogram, not associated with either kinematicdistance (Fig. A2). The associated distance to this dip is D= 10.0 ± V histogram. As there does not appear to be a thirdA V gap in the histogram, it is likely that this prominent A V gap, at A V ∼
11 really is associated with the molecular cloudG031.24-0.01, at a GRS distance of 11.55 kpc. The M06 dataset used is centred at G030.75+00.00 which is ∼ ′ off-centrefrom this third molecular cloud G031.24-0.01. Therefore it ispossible that the M06 data do not represent the line of sightextinction centred on this molecular cloud. For this reasonthe extinction measurement may not have been accuratelyconverted to a distance measurement.This paper has been typeset from a TEX/ L A TEX file preparedby the author. c (cid:13) , 1–18 olecular cloud distance determination from deep NIR survey extinction measurements Figure A1. c (cid:13) , 1–18 Figure A2. c (cid:13)000
11 really is associated with the molecular cloudG031.24-0.01, at a GRS distance of 11.55 kpc. The M06 dataset used is centred at G030.75+00.00 which is ∼ ′ off-centrefrom this third molecular cloud G031.24-0.01. Therefore it ispossible that the M06 data do not represent the line of sightextinction centred on this molecular cloud. For this reasonthe extinction measurement may not have been accuratelyconverted to a distance measurement.This paper has been typeset from a TEX/ L A TEX file preparedby the author. c (cid:13) , 1–18 olecular cloud distance determination from deep NIR survey extinction measurements Figure A1. c (cid:13) , 1–18 Figure A2. c (cid:13)000 , 1–18 olecular cloud distance determination from deep NIR survey extinction measurements Figure A3. c (cid:13) , 1–18 Figure A4. c (cid:13)000
11 really is associated with the molecular cloudG031.24-0.01, at a GRS distance of 11.55 kpc. The M06 dataset used is centred at G030.75+00.00 which is ∼ ′ off-centrefrom this third molecular cloud G031.24-0.01. Therefore it ispossible that the M06 data do not represent the line of sightextinction centred on this molecular cloud. For this reasonthe extinction measurement may not have been accuratelyconverted to a distance measurement.This paper has been typeset from a TEX/ L A TEX file preparedby the author. c (cid:13) , 1–18 olecular cloud distance determination from deep NIR survey extinction measurements Figure A1. c (cid:13) , 1–18 Figure A2. c (cid:13)000 , 1–18 olecular cloud distance determination from deep NIR survey extinction measurements Figure A3. c (cid:13) , 1–18 Figure A4. c (cid:13)000 , 1–18 olecular cloud distance determination from deep NIR survey extinction measurements Figure A5. c (cid:13) , 1–18 Figure A6. c (cid:13)000
11 really is associated with the molecular cloudG031.24-0.01, at a GRS distance of 11.55 kpc. The M06 dataset used is centred at G030.75+00.00 which is ∼ ′ off-centrefrom this third molecular cloud G031.24-0.01. Therefore it ispossible that the M06 data do not represent the line of sightextinction centred on this molecular cloud. For this reasonthe extinction measurement may not have been accuratelyconverted to a distance measurement.This paper has been typeset from a TEX/ L A TEX file preparedby the author. c (cid:13) , 1–18 olecular cloud distance determination from deep NIR survey extinction measurements Figure A1. c (cid:13) , 1–18 Figure A2. c (cid:13)000 , 1–18 olecular cloud distance determination from deep NIR survey extinction measurements Figure A3. c (cid:13) , 1–18 Figure A4. c (cid:13)000 , 1–18 olecular cloud distance determination from deep NIR survey extinction measurements Figure A5. c (cid:13) , 1–18 Figure A6. c (cid:13)000 , 1–18 olecular cloud distance determination from deep NIR survey extinction measurements Figure A7. c (cid:13) , 1–18 Figure A8. c (cid:13)000