Estimators for the exponent and upper limit, and goodness-of-fit tests for (truncated) power-law distributions

Maschberger, Thomas; Kroupa, Pavel

doi:10.1111/j.1365-2966.2009.14577.x

Cited by 66 publications

(70 citation statements)

References 36 publications

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“…In order to determine a mass function for each set of starless cores in our sample, we analysed the cumulative distribution functions of starless core masses for each region in Cepheus, using the maximum likelihood estimator for an infinite power-law distribution (Koen 2006;Maschberger & Kroupa 2009). Throughout the following discussion we assume that the masses of cores can be modelled by a powerlaw function,…”

Section: Discussion Of Derived Propertiesmentioning

confidence: 99%

The JCMT Gould Belt Survey: first results from SCUBA-2 observations of the Cepheus Flare region

Pattle

Ward-Thompson

Kirk

et al. 2016

Mon. Not. R. Astron. Soc.

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We present observations of the Cepheus Flare obtained as part of the James Clerk Maxwell Telescope (JCMT) Gould Belt Legacy Survey (GBLS) with the SCUBA-2 instrument. We produce a catalogue of sources found by SCUBA-2, and separate these into starless cores and protostars. We determine masses and densities for each of our sources, using source temperatures determined by the Herschel Gould Belt Survey. We compare the properties of starless cores in four different molecular clouds: L1147/58, L1172/74, L1251 and L1228. We find that the core mass functions for each region typically show shallower-than-Salpeter behaviour. We find that L1147/58 and L1228 have a high ratio of starless cores to Class II protostars, while L1251 and L1174 have a low ratio, consistent with the latter regions being more active sites of current star formation, while the former are forming stars less actively. We determine that, if modelled as thermally-supported Bonnor-Ebert spheres, most of our cores have stable configurations accessible to them. We estimate the external pressures on our cores using archival 13 CO velocity dispersion measurements and find that our cores are typically pressure-confined, rather than gravitationally bound. We perform a virial analysis on our cores, and find that they typically cannot be supported against collapse by internal thermal energy alone, due primarily to the measured external pressures. This suggests that the dominant mode of internal support in starless cores in the Cepheus Flare is either non-thermal motions or internal magnetic fields.

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Section: Discussion Of Derived Propertiesmentioning

confidence: 99%

The JCMT Gould Belt Survey: first results from SCUBA-2 observations of the Cepheus Flare region

Pattle

Ward-Thompson

Kirk

et al. 2016

Mon. Not. R. Astron. Soc.

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“…Bik et al 2003; Whitmore et al 2010; Chandar et al , 2011, while others say there must be a truncation in the high mass end, best fit by a Schechter function (e.g. Larsen 2009;Gieles et al 2006b;Maschberger & Kroupa 2009). In the latter case, the fit is characterised by a power law at low masses with a truncation at the high mass end and a characteristic truncation mass that varies depending on galactic environment.…”

Section: Cluster Population Propertiesmentioning

confidence: 99%

Properties of the cluster population of NGC 1566 and their implications

Hollyhead

Adamo

Bastian

et al. 2016

Mon. Not. R. Astron. Soc.

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We present results of a photometric study into the cluster population of NGC 1566, a nearby grand design spiral galaxy, sampled out to a Galactocentric radius of ≈ 5.5 kpc. The shape of the mass-limited age distribution shows negligible variation with radial distance from the centre of the galaxy, and demonstrates three separate sections, with a steep beginning, flat middle and steep end. The luminosity function can be approximated by a power law at lower luminosities with evidence of a truncation at higher luminosity. The power law section of the luminosity function of the galaxy is best fitted by an index ≈ −2, in agreement with other studies, and is found to agree with a model luminosity function, which uses an underlying Schechter mass function. The recovered power law slope of the mass distribution shows a slight steepening as a function of galactocentric distance, but this is within error estimates. It also displays a possible truncation at the high mass end. Additionally, the cluster formation efficiency (Γ) and the specific U-band luminosity of clusters (T L (U )) are calculated for NGC 1566 and are consistent with values for similar galaxies. A difference in NGC 1566, however, is that the fairly high star formation rate is in contrast with a low Σ SF R and Γ, indicating that Γ can only be said to depend strongly on Σ SF R , not the star formation rate.

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“…We attempted to ameliorate this issue by also analysing the cumulative distribution function of core masses using the maximum likelihood estimator for an infinite power-law distribution (Koen 2006;Maschberger & Kroupa 2009), calculated over the same mass range (M 0.2M ). The cumulative distribution and fits are shown in Figure 7.…”

Section: Source Mass Distributionmentioning

confidence: 99%

The JCMT Gould Belt Survey: first results from the SCUBA-2 observations of the Ophiuchus molecular cloud and a virial analysis of its prestellar core population

Pattle¹,

Ward-Thompson²,

Kirk³

et al. 2015

Monthly Notices of the Royal Astronomical Society

136

146

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In this paper we present the first observations of the Ophiuchus molecular cloud performed as part of the James Clerk Maxwell Telescope (JCMT) Gould Belt Survey (GBS) with the SCUBA-2 instrument. We demonstrate methods for combining these data with previous HARP CO, Herschel, and IRAM N 2 H + observations in order to accurately quantify the properties of the SCUBA-2 sources in Ophiuchus. We produce a catalogue of all of the sources found by SCUBA-2. We separate these into protostars and starless cores. We list all of the starless cores and perform a full virial analysis, including external pressure. This is the first time that external pressure has been included in this level of detail. We find that the majority of our cores are either bound or virialised. Gravitational energy and external pressure are on average of a similar order of magnitude, but with some variation from region to region. We find that cores in the Oph A region are gravitationally bound prestellar cores, while cores in the Oph C and E regions are pressure-confined. We determine that N 2 H + is a good tracer of the bound material of prestellar cores, although we find some evidence for N 2 H + freezeout at the very highest core densities. We find that non-thermal linewidths decrease substantially between the gas traced by C 18 O and that traced by N 2 H + , indicating the dissipation of turbulence at higher densities. We find that the critical Bonnor-Ebert stability criterion is not a good indicator of the boundedness of our cores. We detect the pre-brown dwarf candidate Oph B-11 and find a flux density and mass consistent with previous work. We discuss regional variations in the nature of the cores and find further support for our previous hypothesis of a global evolutionary gradient across the cloud from southwest to northeast, indicating sequential star formation across the region.

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Estimators for the exponent and upper limit, and goodness-of-fit tests for (truncated) power-law distributions

Cited by 66 publications

References 36 publications

The JCMT Gould Belt Survey: first results from SCUBA-2 observations of the Cepheus Flare region

The JCMT Gould Belt Survey: first results from SCUBA-2 observations of the Cepheus Flare region

Properties of the cluster population of NGC 1566 and their implications

The JCMT Gould Belt Survey: first results from the SCUBA-2 observations of the Ophiuchus molecular cloud and a virial analysis of its prestellar core population

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