Masses and Luminosities of O and B - type stars and red super giants
AAstron. Nachr. / AN , No. 88, 789 – 801 (2010) /
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Masses and Luminosities of O and B - type stars and red super giants
M.M. Hohle , ,(cid:63) , R. Neuh¨auser , and B.F. Schutz , Astrophysical Institute and University-Observatory Jena, Schillerg¨asschen 2-3, 07745 Jena, Germany Max-Planck-Institute for Extraterrestrial Physics, Giessenbachstrasse, 85741 Garching, Germany Max-Planck-Institute for Gravitational Physics Potsdam, Am M¨uhlenberg 1, 14476 Golm, Germany School of Physics and Astronomy, Cardiff University, 5, The Parade, Cardiff, UK, CF24 3AAThe dates of receipt and acceptance should be inserted later
Key words stars: early-type – stars: fundamental parameters – binaries: general – stars: statisticsMassive stars are of interest as progenitors of super novae, i.e. neutron stars and black holes, which can be sources ofgravitational waves. Recent population synthesis models can predict neutron star and gravitational wave observations butdeal with a fixed super nova rate or an assumed initial mass function for the population of massive stars.Here we investigate those massive stars, which are supernova progenitors, i.e. with O and early B type stars, and also allsuper giants within 3kpc. We restrict our sample to those massive stars detected both in 2MASS and observed by Hippar-cos, i.e. only those stars with parallax and precise photometry.To determine the luminosities we calculated the extinctions from published multi-colour photometry, spectral types, lumi-nosity class, all corrected for multiplicity and recently revised Hipparcos distances. We use luminosities and temperaturesto estimate the masses and ages of these stars using different models from different authors.Having estimated the luminosities of all our stars within 3kpc, in particular for all O- and early B-type stars, we have de-termined the median and mean luminosities for all spectral types for luminosity classes I, III, and V. Our luminosity valuesfor super giants deviate from earlier results: Previous work generally overestimates distances and luminosities comparedto our data, this is likely due to Hipparcos parallaxes (generally more accurate and larger than previous ground-based data)and the fact that many massive stars have recently been resolved into multiples of lower masses and luminosities.From luminosities and effective temperatures we derived masses and ages using mass tracks and isochrones from differentauthors. From masses and ages we estimated lifetimes and derived a lower limit for the supernova rate of ≈ events/Myraveraged over the next 10 Myrs within 600 pc from the sun. These data are then used to search for areas in the sky withhigher likelihood for a supernova or gravitational wave event (like OB associations). c (cid:13) To estimate the ages and masses of stars, one almost alwaysneeds their luminosities and temperatures to compare theirlocation in the H-R diagram with theoretical isochrones andtracks. Only in a few rare cases, other mass (or age) esti-mates are possible, e.g. in eclipsing double-lined binaries.Luminosity, mass, and age are very important parameters tostudy and understand the formation of stars. In particular formassive stars, as studied here, the formation mechanism isstill a matter of debate, either accretion from massive disksand/or coagulation of lower- mass stars (see e.g. Zinnecker& Yorke, 2007, for a recent review).For a lot of studies, typical mean luminosities and masses ofstars of a particular spectral type and luminosity class (LC)are necessary, e.g. spectro-photometric distance or mass -luminosity relation.Here, we use Hipparcos (Perryman et al., 1997) parallaxesto re-estimate the luminosities of all massive stars within3kpc, for which both new Hipparcos (van Leeuwen, 2007a,b) and 2MASS (Cutri, 2003) data are available. We useHipparcos/Simbad (BV) and 2MASS (JHK) photometry to- (cid:63)
Corresponding author: [email protected] gether with the known spectral type and luminosity class toestimate the extinction. From these data, we also estimateall luminosities and masses.We restrict our sample to those stars which are assumed tobe progenitors to supernova and/or neutron stars. Data asdetermined in our study are also necessary ingredients topopulation synthesis models to explain current neutron starsobservations and to predict future gravitational wave detec-tions.
We compile a list of all known massive stars, which are sup-posed to explode as supernova (SN), i.e. for LC V and IVspectral types equal or earlier than B4, for LC III equal orearlier than B9 and for LC I and II all spectral types (mas-sive red giants and super giants), all within a distance tothe sun of 3kpc. This distance is chosen, so that we arecomplete for stars earlier than B3V with A V ≤ c (cid:13) a r X i v : . [ a s t r o - ph . S R ] M a r
90 Hohle et al.: Masses and Luminosities of O and B - type stars and red super giants
Table 1
Input data of the first ten stars sorted by ascending relative error of the parallaxes (new reduced Hipparcosparallaxes from van Leeuwen, 2007, corrected using equation 21 in Smith & Eichhorn, 1996). B and V band magnitudesand spectral types are obtained from the Simbad data base (Hipparcos), JHK magnitudes and their errors derived from the2MASS catalogue. If the spectral type is listed in Pourbaix et al. (2007) we give this value. For conversion from spectraltype and luminosity class to temperature see section 4. The complete sample will be available at the ADS data base inelectronic form.
Hip B V J H K π SpType T eff [mag] [mas] [K]1 30122 2.83 3.00 3.464 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± −4 −2 0 2 4 6 8−4−202468 A V using Kenyon & Hartmann/Schmidt−Kaler, B−V [mag] A V u s i ng B esse ll e t a l., B − V [ m a g ] Fig. 1 A V values from single stars calculated from ( B − V ) using the intrinsic colours from different authors. Errorsdenote to σ .Leeuwen, 2007) and 2713 of those Hipparcos stars also haveJHK magnitudes in 2MASS (Two M icron A ll S ky S urvey,Cutri, 2003), searching by the Hipparcos identifier. Somestars (for example Hip 22392 or Hip 23527) from the Mag-ellanic Clouds accidently have parallaxes ≥ , Surkova & Svechnikov (2004)and Perevozkina (1999) listing eclipsing binaries. For 302stars, there is not enough data available on the companion(s)to estimate parameters like luminosity correctly for all com-ponents, so that we omit them from our list. Our list thencontains 2323 (247 multiples + 2076 singles, after check-ing for redundancy) stellar systems, with multiples countedonce, with a total of 2398 stars having all parameters for themass calculation.There are 247 spectroscopic or eclipsing systems in our listfrom the papers mentioned above. All those papers (expectPourbaix et al., 2007) list dynamical masses, which are bet-ter than our model-dependent masses, so that we will usethe published dynamical masses; for the stars in Pourbaix etal. (2007), good photometry is given for all known compo-nents, so that we can estimate the masses for all componentsfrom the published data (as we do for all other stars in ourlist).The input data are listed in Table 1. The 2MASS magnitudes are well measured, with a medianof the relative error of 0.34% for J magnitudes. More than96% of all J magnitudes have errors lower than 10%. Theerrors of the H and K magnitudes are comparable to thosefrom J (Cutri, 2003). We use a general error of 1% for the Band V magnitudes (Simbad and Hipparcos). The calculationof the bolometric corrections from the spectral types andthe extinction ( A V ) due to the interstellar medium followsthe procedure in Hohle et al. (2009) using the bolometriccorrections and the intrinsic colour indices from Bessell etal. (1998), Kenyon & Hartmann (1995) and Schmidt-Kaler(1982). For the spectral types M4-6, we cannot use Bessell For Hip 108317 with ∼ yrs orbit period, Brancewicz & Dworak(1980) did not obtain dynamical masses, so that we obtain and use ownmasses for both components from public data. c (cid:13) stron. Nachr. / AN (2010) 791 −3 −2 −1 0 1 2 3 4 5 6 7 8−3−2−1012345678 A V from V−J [mag] A V f r o m V − H [ m a g ] Fig. 2 A V values from single stars calculated from ( V − J ) and ( V − H ) using the intrinsic colours listed in Kenyon& Hartmann (1995)/Schmidt-Kaler (1982). Errors denote to σ . distance [pc] nu m b e r Fig. 3
Histogram of the new Hipparcos distances (vanLeeuwen, 2007) from all 2323 stars in the final sample(white bars) and after the application of the Smith & Eich-horn (1996) correction (grey), see also Figure 4.et al. (1998), which goes down to 3500K only, so that weuse only Kenyon & Hartmann (1995) and Schmidt-Kaler(1982) for these stars.We calculated the A V values from BVJHK colours of thesingle stars from the final list of 2323 stars and fit them tothe one-to-one relation ( Y ( x ) = Ax + a ) with the resultslisted in Table 2. We only use those colours for our calcu-lations, which are bold faced in Table 2. The criteria forselection is the following: If one linear fit is not consistentto ≥ others, we do not use it, for example ( B − V ) fromKenyon & Hartmann (1995). We treat a linear fit as consis-tent to another one, if A = 1 ± . considering the scattering dA and if a = 0 ± . mag considering da . With this criteriawe select ( V − K ) , ( V − J ) and ( V − H ) from Kenyon& Hartmann (1995)/Schmidt-Kaler (1982). One exceptionis ( V − K ) from Bessell et al. (1998). Although it is notconsistent to more than two linear fits from Bessell et al. parallax [mas] t r a n s f o r m e d p a r a ll ax [ m as ] Fig. 4
Transformation of the Hipparcos parallaxes (vanLeeuwen, 2007) applying the Smith & Eichhorn (1996) cor-rection (red dots) shown with 1 σ error bars from all 2323stars in the final sample. The one-to-one relation is indicatedas dashed line. log (T eff [K]) l og ( L bo l [ L o ]) Fig. 5 H − R diagram of the 2323 stars (dots) in the finallist including 247 resolved massive multiples (grey circles).The large scatter around the main sequence results from theparallax errors. The luminosities were calculated after ap-plying the Smith & Eichhorn (1996) correction. A few bi-naries appear below the main sequence, but are consistent tobeing main sequence within the errors for the luminosities(a representative error bar is shown in the box).(1998), it is consistent to ( V − K ) from Kenyon & Hart-mann (1995), whose consistency is already shown.Generally, the extinctions derived from the different authorsand different magnitudes are well in agreement (see alsoFigures 1-2). The final A V value for each star is calcu-lated from the mean of the A V values from the four coloursmarked bold in Table 2. 109 stars have mean A V values be-low zero (probably due to variability and non-simultaneousphotometry) but all of them are consistent to zero withintheir σ error. We set the A V values for these 109 stars tozero for all further calculations. c (cid:13)(cid:13)
Transformation of the Hipparcos parallaxes (vanLeeuwen, 2007) applying the Smith & Eichhorn (1996) cor-rection (red dots) shown with 1 σ error bars from all 2323stars in the final sample. The one-to-one relation is indicatedas dashed line. log (T eff [K]) l og ( L bo l [ L o ]) Fig. 5 H − R diagram of the 2323 stars (dots) in the finallist including 247 resolved massive multiples (grey circles).The large scatter around the main sequence results from theparallax errors. The luminosities were calculated after ap-plying the Smith & Eichhorn (1996) correction. A few bi-naries appear below the main sequence, but are consistent tobeing main sequence within the errors for the luminosities(a representative error bar is shown in the box).(1998), it is consistent to ( V − K ) from Kenyon & Hart-mann (1995), whose consistency is already shown.Generally, the extinctions derived from the different authorsand different magnitudes are well in agreement (see alsoFigures 1-2). The final A V value for each star is calcu-lated from the mean of the A V values from the four coloursmarked bold in Table 2. 109 stars have mean A V values be-low zero (probably due to variability and non-simultaneousphotometry) but all of them are consistent to zero withintheir σ error. We set the A V values for these 109 stars tozero for all further calculations. c (cid:13)(cid:13)
92 Hohle et al.: Masses and Luminosities of O and B - type stars and red super giants
O9 B0 B1 B2 B3 F2 F5 G0 K3 M222.533.544.555.56 spectral type l og ( L bo l / L o ) LC I
O9 B0 B1 B2 B3 F2 F5 G0 K3 M222.533.544.555.56 spectral type l og ( L bo l / L o ) LC I
O9 B0 B1 B2 B3 B4 B5 B6 B7 B8 B922.533.544.555.56 spectral type l og ( L bo l / L o ) LC III
O9 B0 B1 B2 B3 B4 B5 B6 B7 B8 B922.533.544.555.56 spectral type l og ( L bo l / L o ) LC III
O5 O6 O7 O8 O9 B0 B1 B2 B3 B422.533.544.555.56 spectral type l og ( L bo l / L o ) LC V
O5 O6 O7 O8 O9 B0 B1 B2 B3 B422.533.544.555.56 spectral type l og ( L bo l / L o ) LC V
Fig. 6
Median bolometric luminosities after the application of the Smith & Eichhorn (1996) correction (left panel) fortheir parallax (dots, at least five stars per spectral sub-type) and the median luminosities of the stars from the catalogueof Pourbaix et al. (2007) (squares, at least three stars per spectral sub-type), the dotted lines show the linear interpolationbetween the two subsamples compared to the standard bolometric luminosities from Schmidt-Kaler (1982) as solid lines.The error bars give the standard deviations (in some cases the error bars are smaller than the symbol size). Right panel:same without Smith & Eichhorn (1996) parallax correction. Schmidt-Kaler (1982) overestimates the luminosities due toground based parallaxes and unresolved multiples. c (cid:13) stron. Nachr. / AN (2010) 793 O9 B0 B1 B2 B3 F2 F5 G0 K3 M222.533.544.555.56 spectral type l og ( L bo l / L o ) LC I
O9 B0 B1 B2 B3 F2 F5 G0 K3 M222.533.544.555.56 spectral type l og ( L bo l / L o ) LC I
O9 B0 B1 B2 B3 B4 B5 B6 B7 B8 B922.533.544.555.56 spectral type l og ( L bo l / L o ) LC III
O9 B0 B1 B2 B3 B4 B5 B6 B7 B8 B922.533.544.555.56 spectral type l og ( L bo l / L o ) LC III
O5 O6 O7 O8 O9 B0 B1 B2 B3 B422.533.544.555.56 spectral type l og ( L bo l / L o ) LC V
O5 O6 O7 O8 O9 B0 B1 B2 B3 B422.533.544.555.56 spectral type l og ( L bo l / L o ) LC V
Fig. 7
Same as in Figure 6, but only for those stars within 600 pc. Note that in this case the number of super giants perspectral sub-type is to low for reliable statistics. c (cid:13)(cid:13)
Same as in Figure 6, but only for those stars within 600 pc. Note that in this case the number of super giants perspectral sub-type is to low for reliable statistics. c (cid:13)(cid:13)
94 Hohle et al.: Masses and Luminosities of O and B - type stars and red super giants
Table 2
Results of the fits for the one-to-one relation Y ( x ) = Ax + a of the A V values for single stars using BVJHKmagnitudes and intrinsic colours from Bessell et al. (1998, B98) and a combination from Kenyon & Hartmann (1995) andSchmidt-Kaler (1982) (KH95SK82). B98 A
95% conf. intervall of
A a
95% conf. intervall of a B-V vs
V-K
V-K vs J-H 1.134 (1.099, 1.169) -0.414 (-0.456, -0.372)
V-K vs J-K 1.097 (1.068, 1.126) 0.002 (-0.034, 0.037)J-H vs J-K 0.847 (0.832, 0.862) 0.470 (0.449, 0.490)KH95SK82 A
95% conf. intervall of
A a
95% conf. intervall of a B-V vs V-K 1.030 (1.006, 1.054) 0.182 (0.158, 0.205)B-V vs V-J 1.045 (1.021, 1.068) 0.152 (0.129, 0.175)B-V vs V-K 1.039 (1.015, 1.063) 0.220 (0.197, 0.244)
V-J vs V-H
V-J vs V-K
V-H vs V-K A
95% conf. intervall of
A a
95% conf. intervall of a B-V 0.979 (0.972, 0.987) 0.009 (0.002, 0.017)
V-K
For the resolved 247 binary systems the various catalogueslist spectral types and visual magnitudes for both compo-nents. We estimated the BJHK magnitudes of the compo-nents from the BVJHK magnitudes and the spectral typesof the unresolved system listed in 2MASS and/or Simbadusing the resolved V magnitudes and spectral types given inthe catalogues of both components with a procedure as inHohle et al. (2009).From the resolved BVJHK magnitudes we calculate the A V values using the selected colours mentioned before. Since one does not measure the distance itself, but the par-allaxe, we use the error dependent expectation values of theparallax, which lead to smaller distances. This treatment isintroduced in Smith & Eichhorn (1996). We apply this cor-rection to all stars in our sample using equation 21 in Smith& Eichhorn (1996). The errors of Hipparcos parallaxes areoften as large as its value for a distance of ≥ kpc . Unfor-tunately OB-type stars are typically far from us. 1536 of the2323 stars are within 600pc that is a reliable distance forHipparcos. Due to the small relative errors for this distancesthe Smith & Eichhorn (1996) correction does not stronglyaffect the distance estimate, while for stars with parallaxes ≈ mas this effect becomes important, see Figure 3 and 4.The luminosity of a star in units of L (cid:12) can be calculated bythis familiar equation: L bol = 10 . log d − . − BC V − m V + A V ) (1)with the corrected distance d in parsec.From spectral types we derived the temperatures T eff us-ing the Tables in Bessell et al. (1998), Kenyon & Hartmann R/R o Pasinetti−Fracassini et al. R / R o o w n Fig. 8
Own radii derived from our luminosities and tem-perature from the Stefan-Boltzmann law with σ error barscompared to radii from Pasinetti-Fracassini et al. (2001) cal-culated from intrinsic brightness and colour (stars) and pul-sating stars (squares). Our errors are mainly caused by theerrors of the parallaxes.(1995) and Schmidt-Kaler (1982). With temperature and lu-minosity we show all 2323 stars, singles and massive bina-ries, in the H − R diagram in Figure 5. Our sample containsdozens or even more than hundred stars for most spectraltypes. This enables us to provide reliable statistic medianluminosities with standard deviations for each spectral type(if the given sub-type is not an integer number, for exampleB2.5, we round up to the later spectral type given the slopeof the temperature to spectral type conversion). We comparein Figure 6 our median luminosities with at least five starsper spectral sub-type with previously published (standard)bolometric luminosities from Schmidt-Kaler (1982) listed c (cid:13) stron. Nachr. / AN (2010) 795 Table 3
List of the first ten from 2323 stars (see also Tab. 1). We derived the luminosities from the corrected (Smith& Eichhorn, 1996) parallaxes. From luminosities and effective temperatures we calculated the masses (using the modelsbelow and taking the errors of the luminosities into account) with medians and standard deviation. The complete table willbe available at the ADS data base in electronic form.
Hip L mass[ L (cid:12) ] [ M (cid:12) ]Bertelli et al. (1994) Claret (2004) Schaller et al. (1992) median std. deviation1 30122 3600 7.15-7.60 6.31-7.94 7.00 7.15 0.512 86414 2300 6.35-6.75 6.31 7.00 6.55 0.353 39138 1400 6.05-6.30 6.31 5.00-7.00 6.30 0.754 97278 2500 5.12-5.66 6.26 4.94-4.98 5.66 0.665 69996 2100 6.75-7.00 6.31 7.00 6.80 0.366 99473 848.6 4.18-4.63 3.98-5.01 4.00 4.00 0.357 76600 2704.9 7.25-7.65 7.94 7.00 7.25 0.498 67464 4428.8 8.50-8.80 7.94 9.00 8.50 0.539 79404 2504.2 7.30-7.90 7.94 7.00 7.60 0.4810 32759 18900 10.95-12.90 9.97-12.52 8.97-11.94 11.94 0.49 log (mass/[M o ]) l og ( L bo l / [ L o ]) Fig. 9
We derive a logarithmic slope of . ± . (blacksolid line) for the mass - luminosity relation for main se-quence stars with data listed in Table 4 (filled squares with σ error bars) that is slightly less than the slope of 3.84(dashed line) obtained from the data in Andersen (1991, Ta-ble 1 therein). Hilditch (2001) gives a slope of 4.0 for starswith less than M (cid:12) and 3.6 for stars with larger masses(dotted lines).in Lang (1994).While for most spectral types the values from Schmidt-Kaler (1982) (who do not list errors) are consistent withours, there is a tendency to smaller luminosities for LC Iand III in our new data. This discrepancy is still presentif we restrict our statistics to stars within 600pc (correcteddistances) or use uncorrected parallaxes for the luminosi-ties (because most of the stars are within 600pc where theSmith & Eichhorn (1996) correction is not important, seeFigures 6 and 7).Wegner (2007) calculated luminosities from a star samplewhich is quite similar to ours, but shows only spectral typeslater than A0, with Hipparcos parallax (but extinctions only dynamical mass [M o ] m ass , t h i s w o r k [ M o ] Fig. 10
Masses of both components of binary systems us-ing evolutionary models in this work derived from effectivetemperatures and luminosities (see Brancewicz & Dworak,1980; Bondarenko & Perevozkina, 1996; Perevozkina,1999; Surkova & Svechnikov, 2004) compared to the dy-namical mass values therein. Our mass values are mediansfrom different models (see also Table 3) with the standarddeviations as errors. The dashed line indicates the 1:1 rela-tion: Our masses underestimate the dynamical masses of afactor of 1.5 in median (solid line).from B-V, not from BVJHK) and compared the result tothe luminosities from Schmidt-Kaler (1982). Wegner (2007)found for late type super giants the same differences as we:they are under luminous compared to Schmidt-Kaler (1982)by 1.5 magnitudes in average, in particular also the largediscrepancy around spectral type K and M (up to two mag-nitudes).Recently, photometric distances of 29 OB associations andmany OB field stars were adjusted using Hipparcos paral-laxes from Dambis et al. (2001). They found, that previ-ous photometric distances overestimated the Hipparcos dis-tances about 11% on average for these OB associations and c (cid:13)(cid:13)
Masses of both components of binary systems us-ing evolutionary models in this work derived from effectivetemperatures and luminosities (see Brancewicz & Dworak,1980; Bondarenko & Perevozkina, 1996; Perevozkina,1999; Surkova & Svechnikov, 2004) compared to the dy-namical mass values therein. Our mass values are mediansfrom different models (see also Table 3) with the standarddeviations as errors. The dashed line indicates the 1:1 rela-tion: Our masses underestimate the dynamical masses of afactor of 1.5 in median (solid line).from B-V, not from BVJHK) and compared the result tothe luminosities from Schmidt-Kaler (1982). Wegner (2007)found for late type super giants the same differences as we:they are under luminous compared to Schmidt-Kaler (1982)by 1.5 magnitudes in average, in particular also the largediscrepancy around spectral type K and M (up to two mag-nitudes).Recently, photometric distances of 29 OB associations andmany OB field stars were adjusted using Hipparcos paral-laxes from Dambis et al. (2001). They found, that previ-ous photometric distances overestimated the Hipparcos dis-tances about 11% on average for these OB associations and c (cid:13)(cid:13)
96 Hohle et al.: Masses and Luminosities of O and B - type stars and red super giants
Table 4
From Table 3 we obtain typical error weightedmedian masses and luminosities for different spectral typesand sub-types. We list these masses (together with the lumi-nosities using corrected parallaxes from Figure 6) where atleast five stars for one spectral sub-type are in the sample.Because of uncertain photometry we excluded binaries andall stars listed in Simbad with a range for their possible lu-minosity class. Note that the number of O stars in the sampleis small and that they often have large distances (with largeerrors), i.e. their masses and luminosities are less reliablethan for other spectral types. mass L bol M (cid:12) ] [ M (cid:12) ] [ L (cid:12) ] [ L (cid:12) ]LC IO9 24.25 5.80 146000 13000 9B0 15.00 2.62 27500 1000 27B1 9.97 1.28 14300 300 55B2 8.99 1.35 13400 100 40B3 8.99 2.05 13800 1800 15F5 7.53 2.69 6500 200 6K3 6.26 1.64 3200 200 9M2 2.93 0.75 3900 800 7LC IIIO9 17.77 7.00 43300 8600 6B0 13.75 3.37 18300 2300 16B1 11.98 1.70 12200 600 42B2 7.94 1.01 4900 40 61B3 6.31 0.72 2200 40 68B4 5.01 1.15 1300 50 20B5 5.00 0.51 800 20 83B6 4.65 0.72 580 30 36B7 4.00 0.59 490 10 46B8 4.00 1.23 530 60 11LC VO7 17.52 9.33 13900 700 6O9 19.60 4.33 36400 3100 13B0 15.00 2.83 16100 130 27B1 11.98 1.24 12520 150 81B2 8.50 0.62 4130 60 179B3 6.55 0.42 1770 20 219B4 5.75 0.64 1260 20 71 about 20% for field stars, respectively.With corrected luminosity and effective temperature we canestimate the stellar radius with the Stefan-Boltzman law. Weshow the stellar radii from those stars of our sample whichare listed in Pasinetti-Fracassini et al. (2001) and our ownradii in Figure 8. Pasinetti-Fracassini et al. (2001) providea list of radii measured directly with different methods be-tween 1950 and 1997 (681 values for 246 stars). We see agood consistency of our radii to those of Pasinetti-Fracassiniet al. (2001). With luminosities and effective temperatures, we can esti-mate the masses of our stars by comparing their location inthe H-R diagram with model mass tracks. We use evolution-ary models from Schaller et al. (1992), Bertelli et al. (1994)and Claret (2004). The different authors provide evolution-ary tracks for different metallicities, we present the massesfor solar metallicity. The metallicity is only well known forfew stars and affect the mass estimation only by a few per-cent. The differences in mass between the models with thesame metallicities are comparable to this.Owing to the discrepancies in the luminosities for super gi-ants, we fix the temperature first, that is much better knownthan the luminosity, within 10% tolerance taking possibleuncertainties from the spectral type determination into ac-count. We then determined the mass tracks with the bestrelative agreement to the given luminosities within their er-rors. Even if the luminosity is strongly underestimated andthe relative deviation to the nearest mass track will be large,at least it will be on the main sequence. This avoids a sys-tematic underestimation of the masses caused from under-estimated luminosities.The models of Schaller et al. (1992) underestimate the massesby 0.37% in median compared to the masses obtained fromBertelli et al. (1994), while Clarets (2004) model overes-timates the masses about 2.7% in median compared to themasses from the model of Bertelli et al. (1994), i.e. theyagree well. While Claret (2004) and Schaller et al. (1992)provide models for masses up to M (cid:12) , the models fromBertelli et al. (1994) give masses up to M (cid:12) for solarmetallicity. Therefore, if the mass estimation of a star usingSchaller et al. (1992) or Claret (2004) results in M (cid:12) ormore, we did not use the results using Bertelli et al. (1994).We list the results of the first ten stars in Table 3.Using the different results from the different models foreach star, we find, that the mean of the standard derivation is9.9% compared to the median of the masses themselves. Wesee this as good consistency. For 76% of the stars, the stan-dard deviation of the mass is less than 10% of the medianof the mass value and for 28% of the stars the standard de-viation is less than 5%. The standard deviations of the massvalues may underestimate the error of mass estimation.Having determined the masses of all 2323 stars, we ob-tain median masses for the spectral sub-types depending onthe LC. Likewise for the bolometric luminosities we havedozens, or even more than hundred, stars per spectral sub-type, i.e. the median masses should be robust against fluctu-ations and errors in the empirical data. We list these massesfor stars with at least five entries in a spectral sub-type inTable 4. If a system appears in one of the used binary cat-alogues, we use its dynamical mass instead of our model-dependent masses. If one system appears in more than oneof these catalogues, we use the median and the standard de-viation (as error) from the different mass values.From masses and luminosities in Table 4 we derive a mass- luminosity relation ( L ∝ M β ) with β = 3 . ± . for c (cid:13) stron. Nachr. / AN (2010) 797 Table 5
List of 36 binary systems where both components exceed 8 M (cid:12) from dynamical masses given in the binary cat-alogues discussed in the text (see also column seven). We list mass and spectral type ranges obtained from these cataloguesfor both components. Hip SpType mass/[ M (cid:12) ] ref.primary secondary primary secondary1 1415 O7/O9III O8-9/O9III 20.30-57.75 14.8-31.73 [1], [2], [4]2 4279 A5I G0I 19.88 9.94 [2]3 15063 O9.3IV O9IV 20.37 9.98 [2], [4]4 25565 B0V/O9.5V B1/B2/B0.5 12.04-21.30 7.95-14.50 [1], [2], [4]5 25733 O9.5/O9.5III B0IV/09.5III 21.28-24.00 12.7-18.90 [1], [2], [4]6 28045 B4V/F3eIb K5II 18.46 11.08 [2], [4]7 29276 B3III/B1V/B0.5III B3.5/B3V 15.48-16.90 8.51-9.00 [1], [2], [4]8 31939 B1.5IV B3 11.50 8.40 [1]9 33953 B2.5IV/B2.5IV-V B2.5IV-V 15.35 15.35 [2], [4]10 34646 B3 B4 11.10 8.88 [2]11 35412 O7 O9III/O7.5 22.00 18.30 [1], [2], [4]12 56196 B5-O7 B8-O9.5 8.24-22.60 7.75-15.40 [2], [4], [5]13 57895 B1III ? 14.58 10.21 [2]14 59483 G2I ? 11.67 8.17 [2]15 85985 B1V B1.5 10.30 10.20 [1]16 89769 WC7-8 B0/O8-9III-V 18.49 11.28 [2], [4]17 92055 B3 B3 22.39 15.01 [2]18 92865 O9/O9V B1-3/B3V 18.01-38.20 10.81-13.80 [1], [2], [4]19 93502 B2/B3.5/B4V B3.5-8 18.03-18.40 11.36-11.40 [1], [2], [4]20 95176 A5I M5Ia 25.18 19.14 [2]21 97634 B1.5II-III/B1III B2-3V 16.70 9.35 [2], [4]22 99021 O9.5e/O9.5V/O8.9V B1I-II/B1Ib/B1.2Ib 23.84-25.20 14.00-15.73 [2], [3]23 100135 O6.5/O6.5V/O7.5 O7.5/O9 28.00-37.16 19.60-32.70 [1], [2], [4]24 100193 B2 B2/B2.5 13.82 12.16 [2], [4]25 100214 WN5-5.5 B1/O8III 34.53 19.34 [2], [4]26 101341 O7/O7f O9-B0/O8 26.70-27.80 6.70-22.96 [1], [2]27 102648 A5Iab/A5epIa A9 12.62 8.83 [2], [4]28 102999 B0IV B0IV 17.71 17.53 [2], [4]29 103419 K5I B4V 22.64 8.1504 [2]30 108073 B0.5V B1V 10.51 9.46 [2]31 108317 M2epIa B8Ve/B9 63.81 35.10 [2], [4]32 110154 WN6 B0III 23.95 16.05 [2]33 112470 O5 O5 34.00 27.70 [1]34 112562 B0.5V/O8 B0.5V/B0.5/O9 15.22-18.10 13.24-15.90 [1], [2], [4]35 113461 B0IV B0IV 16.07 13.98 [2], [4]36 113907 B0.5/B0.5IV-V B0.5IV-V 10.62 9.45 [2], [4][1] Bondarenko & Perevozkina (1996)[2] Brancewicz & Dworak (1980)[3] Surkova & Svechnikov (2004)[4] Pourbaix et al. (2007)[5] Docobo & Andrade (2006) the main sequence stars (see Figure 9).We also compare the masses of the binaries with dynamicalmasses with our method of mass determination. We use theeffective temperatures and luminosities (derived from M bol )listed in Brancewicz & Dworak (1980), effective temper-atures from listed spectral types and luminosities (derivedfrom M bol ) in Bondarenko & Perevozkina (1996), Perevozk-ina (1999) and Surkova & Svechnikov (2004) to calculateown mass values (if a system appears in more than onecatalogue we list the median of the different masses). Ourmasses are in good agreement but tend to smaller values (afactor of 1.5 in median, peak at ≈ − ) compared to the masses from the other authors (see Figure 10). We find 759 stars in our sample with median masses ≥ M (cid:12) in total, 36 of them are the secondaries of a more mas-sive primary (Table 5). Among them, in three systems theprimary has a median mass ≥ M (cid:12) , i.e. may form a blackhole. We list current masses in Table 5, but do not include c (cid:13)(cid:13)
List of 36 binary systems where both components exceed 8 M (cid:12) from dynamical masses given in the binary cat-alogues discussed in the text (see also column seven). We list mass and spectral type ranges obtained from these cataloguesfor both components. Hip SpType mass/[ M (cid:12) ] ref.primary secondary primary secondary1 1415 O7/O9III O8-9/O9III 20.30-57.75 14.8-31.73 [1], [2], [4]2 4279 A5I G0I 19.88 9.94 [2]3 15063 O9.3IV O9IV 20.37 9.98 [2], [4]4 25565 B0V/O9.5V B1/B2/B0.5 12.04-21.30 7.95-14.50 [1], [2], [4]5 25733 O9.5/O9.5III B0IV/09.5III 21.28-24.00 12.7-18.90 [1], [2], [4]6 28045 B4V/F3eIb K5II 18.46 11.08 [2], [4]7 29276 B3III/B1V/B0.5III B3.5/B3V 15.48-16.90 8.51-9.00 [1], [2], [4]8 31939 B1.5IV B3 11.50 8.40 [1]9 33953 B2.5IV/B2.5IV-V B2.5IV-V 15.35 15.35 [2], [4]10 34646 B3 B4 11.10 8.88 [2]11 35412 O7 O9III/O7.5 22.00 18.30 [1], [2], [4]12 56196 B5-O7 B8-O9.5 8.24-22.60 7.75-15.40 [2], [4], [5]13 57895 B1III ? 14.58 10.21 [2]14 59483 G2I ? 11.67 8.17 [2]15 85985 B1V B1.5 10.30 10.20 [1]16 89769 WC7-8 B0/O8-9III-V 18.49 11.28 [2], [4]17 92055 B3 B3 22.39 15.01 [2]18 92865 O9/O9V B1-3/B3V 18.01-38.20 10.81-13.80 [1], [2], [4]19 93502 B2/B3.5/B4V B3.5-8 18.03-18.40 11.36-11.40 [1], [2], [4]20 95176 A5I M5Ia 25.18 19.14 [2]21 97634 B1.5II-III/B1III B2-3V 16.70 9.35 [2], [4]22 99021 O9.5e/O9.5V/O8.9V B1I-II/B1Ib/B1.2Ib 23.84-25.20 14.00-15.73 [2], [3]23 100135 O6.5/O6.5V/O7.5 O7.5/O9 28.00-37.16 19.60-32.70 [1], [2], [4]24 100193 B2 B2/B2.5 13.82 12.16 [2], [4]25 100214 WN5-5.5 B1/O8III 34.53 19.34 [2], [4]26 101341 O7/O7f O9-B0/O8 26.70-27.80 6.70-22.96 [1], [2]27 102648 A5Iab/A5epIa A9 12.62 8.83 [2], [4]28 102999 B0IV B0IV 17.71 17.53 [2], [4]29 103419 K5I B4V 22.64 8.1504 [2]30 108073 B0.5V B1V 10.51 9.46 [2]31 108317 M2epIa B8Ve/B9 63.81 35.10 [2], [4]32 110154 WN6 B0III 23.95 16.05 [2]33 112470 O5 O5 34.00 27.70 [1]34 112562 B0.5V/O8 B0.5V/B0.5/O9 15.22-18.10 13.24-15.90 [1], [2], [4]35 113461 B0IV B0IV 16.07 13.98 [2], [4]36 113907 B0.5/B0.5IV-V B0.5IV-V 10.62 9.45 [2], [4][1] Bondarenko & Perevozkina (1996)[2] Brancewicz & Dworak (1980)[3] Surkova & Svechnikov (2004)[4] Pourbaix et al. (2007)[5] Docobo & Andrade (2006) the main sequence stars (see Figure 9).We also compare the masses of the binaries with dynamicalmasses with our method of mass determination. We use theeffective temperatures and luminosities (derived from M bol )listed in Brancewicz & Dworak (1980), effective temper-atures from listed spectral types and luminosities (derivedfrom M bol ) in Bondarenko & Perevozkina (1996), Perevozk-ina (1999) and Surkova & Svechnikov (2004) to calculateown mass values (if a system appears in more than onecatalogue we list the median of the different masses). Ourmasses are in good agreement but tend to smaller values (afactor of 1.5 in median, peak at ≈ − ) compared to the masses from the other authors (see Figure 10). We find 759 stars in our sample with median masses ≥ M (cid:12) in total, 36 of them are the secondaries of a more mas-sive primary (Table 5). Among them, in three systems theprimary has a median mass ≥ M (cid:12) , i.e. may form a blackhole. We list current masses in Table 5, but do not include c (cid:13)(cid:13)
98 Hohle et al.: Masses and Luminosities of O and B - type stars and red super giants -75 (cid:176) -60 (cid:176) -45 (cid:176) -30 (cid:176) -15 (cid:176) (cid:176) +15 (cid:176) +30 (cid:176) +45 (cid:176) +60 (cid:176) +75 (cid:176) l=0°30°90° 60°120°150° 210°240°270°300°330° CygCepCam/CasPer Vela OriSco Cen LMCSMC
Fig. 11
The complete star sample used in this work is represented by grey dots. Massive binaries are shown as blackdots (with both components having masses ≥ M (cid:12) ) from dynamical masses listed in Brancewicz & Dworak (1980), Bon-darenko & Perevozkina (1996), Perevozkina (1999) and Surkova & Svechnikov (2004). We indicate a few OB associations,where we find clusters of massive stars, i.e. predict more supernovae in the near future (see Figure 13). Both MagellanicClouds (LMC and SMC) are indicated, which were left out for this work.binary interaction for predicting the final outcome.Starting from the median mass values with the standarddeviations ( σ ) as errors we can give a maximum numberof such systems (median + σ ), a median number (medianmasses) and a minimum number (median - σ ), see Table6. We also give the corresponding numbers for these pro-genitors within 600pc in Table 6. This includes the GouldBelt that hosts 2/3 of the SN progenitors within this dis-tance (Torra et al., 2000).From the mass estimation we also obtain ages using thecorresponding isochrones in the models. Given masses andages we estimate the expected remaining life time of a starusing the model in Maeder & Meynet (1989) and, hence,predict a SN rate for the near future (that should be simi-lar to the SN rate of the recent past). This SN rate is stableuntil ∼ ± ± ± Our mean luminosities and masses are derived from dozensof stars for most spectral types, which should make our re-sults reliable and robust against individual outliers. In oursample 1536 stars are within 600pc and 2127 stars are within c (cid:13) stron. Nachr. / AN (2010) 799 time [Myrs] S N r a t e / M y r Fig. 12
The supernova rate within 600 pc in the fu-ture (circles) obtained from the stars of our sample andmultiplied with 2/3 (squares) for the Gould Belt rate(see text) compared with the rate of 20-27 events/Myrgiven in Grenier (2000) for the Gould Belt (dashed lines).Due to our selection criteria (see text) for the star sam-ple, our rate is a lower limit. The average rate over10Myrs is ≥ ± ≥ ± Table 6
Number of systems with at least one neutron star(NS) or black hole (BH) progenitor in the total sample (seetext) and within 600pc in parenthesis plus the correspond-ing number if both components of a binary system are NSand/or BH progenitors. The numbers are obtained from themedian mass values (median numbers), the minimum (me-dian mass value - σ ) and the maximum (median mass value+ σ ) numbers of progenitors. minimum median maximumNS prog. within 3kpc 686 + 26 759 + 36 1004 + 43within 0.6kpc (287 + 12) (356 + 19) (485 + 25)BH prog. within 3kpc 12 + 1 24 + 1 54 + 3within 0.6kpc (2 + 0) (2 + 0) (8 + 0) σ error or to stars closer than 600pc.This has several reasons:1. Hipparcos distances are smaller than previously usedground based distances. This effect of 20 - 30% in dis-tance results in a revision of luminosity of 44 - 70%. Wethereby confirm previous similar conclusions by Dambiset al. (2001) and Wegner (2007).2. Many stars, especially super giants, which were sup-posed to be single stars decades ago, are now knownas multiple or double systems with their components on the main sequence. Schmidt-Kaler (1982) uses datafrom Code et al. (1976). 75% of the stars in Code et al.(1976) are known to be binaries or multiples today, butlisted as single stars in Code et al. (1976). The masses we derived from our new luminosities us-ing evolutionary models agree well with dynamical masses.We find 36 binaries with both components ≥ M (cid:12) and es-timated the SN rate for the next 10Myrs for the solar neigh-bourhood to be about one SN per 50kyr. We have restrictedour sample here to those massive stars within 3kpc, whichhave both Hipparcos parallax and 2MASS JHK data. Wewill enlarge our sample including all possible super novaprogenitors within 3kpc in further work.Information about the likely distribution of neutron starsin the solar neighborhood can be important for the designof searches for gravitational waves (GWs) with current in-terferometric detectors like GEO600, LIGO and VIRGO.Blind searches for previously unknown neutron stars radiat-ing gravitational waves are computationally very expensive,so restriction of searches to specific regions of the sky, fre-quencies, and spin-down time-scales can improve the sensi-tivity of searches. Of particular interest in current searchesare old, isolated neutron stars which have cooled down sothat they are no longer visible as X-ray sources, and whichmight not be radio pulsars or might have pulsar beams thatare not directed toward us. Taking high kick velocities intoaccount, 140 neutron stars, younger than 4 Myrs, should bestill present within 1 kpc (Palomba, 2005).Current GW searches for isolated neutron stars contain aspin-down parameter, which means that they can also detectaccelerating systems, such as sources in wide binary sys-tems. GW searches could easily be generalized to find neu-tron stars in wide binaries, even potentially those with ac-cretion that leads to increased ellipticity and spin-up ratherthan spin-down. Acknowledgements.
The work is supported by the Deutsche Forschungs-gemeinschaft (DFG) through SFB/TR 7 ”Gravitationswellenastronomie”.We would like to thank B. Allen, B. Owen, K. Schreyer, B. Posseltand A. Seifahrt for helpful discussions. One of those stars is HD 68273, which was known as WC8 + O9I(in Code at al., 1976) and is now known as O9 + B3 + A0 + A0 (CCDMcatalogue, C atalogue of the C omponents of the D ouble and M ultiple stars,Dommanget & Nys, 2000). The magnitudes M V ( W C and M V ( O I ) were measured as ( − . ± . mag and ( − . ± . mag , respectively,from Conti & Smith (1972). The distance was assumed to be 460pc inAbt et al. (1976) but was revised to 258pc in van der Hucht et al. (1997)using the Hipparcos parallax. The new distance yields to M V ( W C
8) = − . mag and M V ( O I ) = − mag . c (cid:13)(cid:13)
8) = − . mag and M V ( O I ) = − mag . c (cid:13)(cid:13)
00 Hohle et al.: Masses and Luminosities of O and B - type stars and red super giants -75 (cid:176) -60 (cid:176) -45 (cid:176) -30 (cid:176) -15 (cid:176) (cid:176) +15 (cid:176) +30 (cid:176) +45 (cid:176) +60 (cid:176) +75 (cid:176) CygCepCam/CasPer Vela OriSco Cen
Fig. 13
Same as in Figure 11, shown with the distribution of the super nova rate for the next 10 Myrs (see also Figure 12)including all massive stars within 600pc. The colours indicate the normalised rate per Myr and square bin (longitude andlatitude both divided in 25 bins). Note, that the super nova rate per area in Orion is 2-3 times higher than for the otherclusters.
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