Extinction. The dodo What makes species vulnerable to extinction?
Completeness of the CMFs derived from extinction data...shown in the top left panel (LAL06). Other...
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Completeness of the CMFs derived from extinction data Kainulainen, J. (1),(2) , Alves, J. (3) ., Lada, C. J. (4) , Rathborne, J. (4) (1) TKK/Metsähovi Radio Observatory, Metsähovintie 114, FIN-02540 Kylmälä, Finland (2) HU Observatory, P.O. Box 14, FIN-00014 University of Helsinki, Finland (3) Calar Alto Observatory, Centro Astronomico Hispano, Alemán, C/q Jesús Durbán Remón 2-2, 04004 Almeria, Spain (4) Harvard-Smithsonian Center for Astrophysics, Mail Stop 72, 60 Garden Street, Cambridge, MA 02138, USA Abstract We examine the completeness of the dense core mass functions (CMFs) derived for molecular clouds using extinction data and the core iden- tification scheme adopted recently by Alves et al. (2007) to derive the CMF of the Pipe nebula. We find that the completeness of the observed CMF depends on the parameters selected for the core extraction algorithm. More importantly, it de- pends on how crowded the core population is. The observed CMF recovers the true CMF reli- ably if the mean separation of the cores is larger than the mean diameter of the cores (f 1), in which case the 90 % completeness level of the observed CMF is at 0.8 ... 1.5 M . Provided that f 1.5, the masses of individual cores are recov- ered with the typical uncertainty of 30 %. Introduction Near infrared extinction data provides probably the most accurate and efficient way to trace the col- umn density distribution of a molecular cloud over a large spatial and dynamical scale. This gives a healthy ground to exploit extinction data to study the mass function of the dense cores in the cloud. However, the derivation of the CMF based on ex- tinction data alone is expected to be hampered by difficulties in identifying the cores from the 2- dimensional data. In this work we study the com- pleteness of the observed CMFs by simulating the core identification process. Simulations In the simulations populations of artificial cores were embedded into the diffuse and spatially vari- able extinction component of the Pipe nebula. The cores were extracted from this simulated extinction data, and the CMF constructed from the extracted cores was compared to the input mass function. The core extraction was repeated using several pa- rameter sets for the core identification algorithm. We also performed simulations with different in- put CMFs and different levels of core crowding. The background component: We used real extinction data of the Pipe (LAL06) to create the background component for the simulations (Fig 1). The cores initially present in the data were elim- inated with a wavelet decomposition technique that effectively filters the small-scale structures out of the map. The remaining large-scale component was used as the background extinction component in the simulations. The population of cores: The artificial core populations were composed of elliptical Gaussians embedded into the background component. The positions of the cores were chosen randomly, but weighted with the spatial density function of the real cores in the Pipe nebula. We used the ratio f = mean core separation / mean core diameter as a metric to describe the core crowding. We gener- ated distributions where f =2, 1.5, 1, and 0.5, and a distribution where the cores were positioned into a rectangular grid. The core extraction: Following ALL07, the core extraction was made in two steps. First, the small-scale structures were identified using a wavelet decomposition technique. Second, the cores were extracted from the decomposed map using the clfind2d procedure (Williams et al. 1994). Figures Fig. 1: Illustration of the simulated extinction data. The original extinction map of the Pipe nebula is shown in the top left panel (LAL06). Other panels show simulated extinction maps that are composed of the extended background component of the Pipe nebula and of a population of artificial cores. Each panel shows simulation with different ratio of mean core separation to mean core diameter (f ). The clfind2d parameter sets: # A th V [σ rms ] a δ A V [σ rms ] b 3 3 7 5 3 3 9 1 3 Fig. 2: Examples of the observed (black) and input (red) CMFs in a simulation where the cores were positioned into a fixed grid pat- tern to prevent overlaps. Fig. 3: Examples of the observed (black) and input (red) CMFs for simulations with different levels of crowding (f =2.0, 1.5, 1.0, and 0.5) Fig. 4: The frequency distribu- tions of M observed /M input ratio for simulations with five different levels of crowding: no overlaps, f =2.0, 1.5, 1.0, and 0.5. Results Completeness levels: Figure 2 shows examples of the CMFs resulting from the simulations where the cores did not over- lap. The exponents of the input CMFs were Γ= -1 and Γ =[ -0.3, -1.35] with the breakpoint at 3 M . Generally, the simulations recover the input CMFs well above the limiting mass, below which the ob- served CMF becomes flatter than the input CMF. These completeness limits, located at M ≈ 0.6 ... 1.2 M , are not affected by crowding, and thus reflect the accuracy at which the method is able disentan- gle cores from the background. The major factor affecting the recoverability of the CMF is the crowding of cores. Figure 3 shows examples of the CMFs for simulations where the core crowding was altered. In the most sparse simulations where f =2, the CMFs are well re- covered above M> 0.8 ... 1.5 M , depending on the parameters chosen for clfind2d algorithm. In simulations where f =1, the observed CMFs are more clearly altered, which is seen as an overabun- dance of cores at intermediate mass bins. This de- fect is more apparent when the masses of the ob- served cores are compared to their input masses (see next section). In the most crowded simulation with f =0.5 the observed CMFs recover the un- derlying mass function very inaccurately. The accuracy of detected masses: We calculated the ratio of input and output masses, M observed /M input , for each input core. The fre- quency distributions of the ratios for one series of simulations are shown in Fig. 4. The figure shows histograms for five crowding levels: no overlaps, and f =2.0, 1.5, 1.0, and 0.5. There is large differences in the histograms between the simulations with different levels of crowding. In the simulations with no overlaps, the shape of the distribution is nearly Gaussian. When the crowding is more severe (f =1.5 and f =1.0) the distribution is wider and the tail to- wards higher ratios becomes more prominent. In the most crowded simulations where f =0.5 the distribution is clearly different from the previous cases, being exceedingly wide and elongated. Finally, we note that for the cores detected in the Pipe nebula by ALL07 the ratio f ≈ 2. On the basis of the simulations, we conclude that the break in the power-law occuring at M =2 ... 3 M is not an artifact caused by the extraction method. References [1] Alves, J. et al. 2007, A&A, 462, L17, ALL07 [2] Lombardi, M. et al. 2006, A&A, 454, 781, LAL06 [3] Williams, J. P et al. 1994, ApJ, 428, 693 Poster template credit: Brian Amberg
Transcript of Completeness of the CMFs derived from extinction data...shown in the top left panel (LAL06). Other...
Completeness of the CMFs derived from extinction dataKainulainen, J.(1),(2), Alves, J.(3)., Lada, C. J.(4), Rathborne, J.(4)
(1) TKK/Metsähovi Radio Observatory, Metsähovintie 114, FIN-02540 Kylmälä, Finland(2) HU Observatory, P.O. Box 14, FIN-00014 University of Helsinki, Finland
(3) Calar Alto Observatory, Centro Astronomico Hispano, Alemán, C/q Jesús Durbán Remón 2-2, 04004 Almeria, Spain(4) Harvard-Smithsonian Center for Astrophysics, Mail Stop 72, 60 Garden Street, Cambridge, MA 02138, USA
AbstractWe examine the completeness of the dense coremass functions (CMFs) derived for molecularclouds using extinction data and the core iden-tification scheme adopted recently by Alves et al.(2007) to derive the CMF of the Pipe nebula. Wefind that the completeness of the observed CMFdepends on the parameters selected for the coreextraction algorithm. More importantly, it de-pends on how crowded the core population is.The observed CMF recovers the true CMF reli-ably if the mean separation of the cores is largerthan the mean diameter of the cores (f ! 1), inwhich case the 90 % completeness level of theobserved CMF is at 0.8 . . . 1.5 M!. Provided thatf ! 1.5, the masses of individual cores are recov-ered with the typical uncertainty of 30 %.
IntroductionNear infrared extinction data provides probablythe most accurate and efficient way to trace the col-umn density distribution of a molecular cloud overa large spatial and dynamical scale. This gives ahealthy ground to exploit extinction data to studythe mass function of the dense cores in the cloud.However, the derivation of the CMF based on ex-tinction data alone is expected to be hamperedby difficulties in identifying the cores from the 2-dimensional data. In this work we study the com-pleteness of the observed CMFs by simulating thecore identification process.
SimulationsIn the simulations populations of artificial coreswere embedded into the diffuse and spatially vari-able extinction component of the Pipe nebula. Thecores were extracted from this simulated extinctiondata, and the CMF constructed from the extractedcores was compared to the input mass function.The core extraction was repeated using several pa-rameter sets for the core identification algorithm.We also performed simulations with different in-put CMFs and different levels of core crowding.The background component: We used realextinction data of the Pipe (LAL06) to create thebackground component for the simulations (Fig 1).The cores initially present in the data were elim-inated with a wavelet decomposition techniquethat effectively filters the small-scale structures outof the map. The remaining large-scale componentwas used as the background extinction componentin the simulations.The population of cores: The artificial corepopulations were composed of elliptical Gaussiansembedded into the background component. Thepositions of the cores were chosen randomly, butweighted with the spatial density function of thereal cores in the Pipe nebula. We used the ratio f= mean core separation / mean core diameter asa metric to describe the core crowding. We gener-ated distributions where f = 2, 1.5, 1, and 0.5, anda distribution where the cores were positioned intoa rectangular grid.The core extraction: Following ALL07, thecore extraction was made in two steps. First,the small-scale structures were identified using awavelet decomposition technique. Second, thecores were extracted from the decomposed mapusing the clfind2d procedure (Williams et al. 1994).
Figures
Fig. 1: Illustration of the simulated extinction data. The original extinction map of the Pipe nebula isshown in the top left panel (LAL06). Other panels show simulated extinction maps that are composedof the extended background component of the Pipe nebula and of a population of artificial cores. Eachpanel shows simulation with different ratio of mean core separation to mean core diameter (f ).
The clfind2d parameter sets:
J. Kainulainen et al.: The completeness of the core mass functions derived from near-infrared extinction data 3
Fig. 1. Top Left: The extinction map of the Pipe Nebula, as presented in LAL06. The average separation to diameter ratio of the coresdetected by ALL07 is f = 2.0 Top Right: An example of the extinction map used in the simulations. The map is composed of a diffusebackground component similar to the large-scale structure of the Pipe nebula, and of a population of artificial cores (elliptical Gaussians). Thefigure corresponds to the simulation where Γ = −1 and f = 1.5. Bottom Left: The same, but for simulation where f = 1.0. Bottom Right: Thesame, but for simulation where f = 0.5.
Table 1. The parameter sets used in the core extraction.
# AthV[σrms]a δAV [σrms]b
3 3 75 3 39 1 3
a The detection threshold of the core extraction algorithmb The contour level spacing
3. Results
3.1. The detectability of cores
Our first goal is to study how well the cores can be identi-fied from the variable background extinction using the methodadopted in this paper. To do this, the crowding of cores needs tobe eliminated from the simulations. When the crowding is notaffecting the observed CMF, possible inaccuracy of the CMFresults from the inability of the method to disentangle the coresfrom the background map. For this purpose, we performed a se-ries of simulations where the the cores were positioned into afixed grid pattern in which the cores certainly do not overlap. Inevery other respect the simulations were performed as explainedin Section §??. We also studied how the choice of the core ex-traction parameter set affected the appearance of the CMFs inthese simulations.
Figure ?? shows the CMFs resulting from this experiment.The three columns of the figure correspond to the simulationswhere the exponents of the input CMFs were Γ = −1, Γ = 0, andΓ = [−0.3,−1.35] with the breakpoint at 3 M". The three rowscorrespond to the CMFs derived using parameter sets #3, #5,and #9. The histograms of the input CMFs are also plotted in thepanels. The mass bins belowwhich the observed CMFs are morethan 10 % below the input CMFs are marked in Fig. ?? with ver-tical lines. Generally, the simulations recover the shape of theinput mass function well above the limiting mass, below whichthe observed CMF becomes flatter than the input CMF. Thesecompleteness limits are not affected by crowding, and thus theyreflect the accuracywith which the adoptedmethod is able repro-duce the underlying CMF (note the discussion regarding theselimits presented later in this section).
The completeness limits of the simulations in this experi-ment vary from M ≈ 0.6 M" for sets #7-#10 to M ≈ 1.2 M"for sets #1-#6. Thus, it appears that the CMF is recovered over alarger range when choosing lower thresholds and narrower levelspacings for the extraction algorithm. However, it is noteworthythat there is only very subtle differences in the observed CMFsin the mass range where the CMF is recovered well with all pa-rameter sets, i.e. at M > 1.2 M". This is encouraging, becauseit means that for the cores above that mass the selection of coreextraction parameters is a minor issue. Above the completenesslimits the exponents of the CMFs are also accurately recovered,which was verified by fitting a power-law to the observed mass
Fig. 2: Examples of the observed(black) and input (red) CMFs in asimulation where the cores werepositioned into a fixed grid pat-tern to prevent overlaps.
Fig. 3: Examples of the observed(black) and input (red) CMFs forsimulations with different levelsof crowding (f = 2.0, 1.5, 1.0, and0.5)
Fig. 4: The frequency distribu-tions of Mobserved/M input ratiofor simulations with five differentlevels of crowding: no overlaps,f = 2.0, 1.5, 1.0, and 0.5.
ResultsCompleteness levels:Figure 2 shows examples of the CMFs resultingfrom the simulations where the cores did not over-lap. The exponents of the input CMFs were Γ = −1and Γ =[ −0.3,−1.35] with the breakpoint at 3 M!.Generally, the simulations recover the input CMFswell above the limiting mass, below which the ob-served CMF becomes flatter than the input CMF.These completeness limits, located at M ≈ 0.6 . . . 1.2M!, are not affected by crowding, and thus reflectthe accuracy at which the method is able disentan-gle cores from the background.
The major factor affecting the recoverability ofthe CMF is the crowding of cores. Figure 3 showsexamples of the CMFs for simulations where thecore crowding was altered. In the most sparsesimulations where f = 2, the CMFs are well re-covered above M > 0.8 . . . 1.5 M!, depending onthe parameters chosen for clfind2d algorithm. Insimulations where f = 1, the observed CMFs aremore clearly altered, which is seen as an overabun-dance of cores at intermediate mass bins. This de-fect is more apparent when the masses of the ob-served cores are compared to their input masses(see next section). In the most crowded simulationwith f = 0.5 the observed CMFs recover the un-derlying mass function very inaccurately.
The accuracy of detected masses:We calculated the ratio of input and output masses,Mobserved/M input, for each input core. The fre-quency distributions of the ratios for one series ofsimulations are shown in Fig. 4. The figure showshistograms for five crowding levels: no overlaps,and f = 2.0, 1.5, 1.0, and 0.5.
There is large differences in the histogramsbetween the simulations with different levels ofcrowding. In the simulations with no overlaps,the shape of the distribution is nearly Gaussian.When the crowding is more severe (f = 1.5 andf = 1.0) the distribution is wider and the tail to-wards higher ratios becomes more prominent. Inthe most crowded simulations where f = 0.5 thedistribution is clearly different from the previouscases, being exceedingly wide and elongated.
Finally, we note that for the cores detected in thePipe nebula by ALL07 the ratio f ≈ 2. On the basisof the simulations, we conclude that the break inthe power-law occuring at M = 2 . . . 3 M! is notan artifact caused by the extraction method.
References[1] Alves, J. et al. 2007, A&A, 462, L17, ALL07[2] Lombardi, M. et al. 2006, A&A, 454, 781, LAL06[3] Williams, J. P et al. 1994, ApJ, 428, 693
Poster template credit: Brian Amberg
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