The Initial Mass Function of Stars: Evidence for Uniformity in Variable Systems Pavel Kroupa

Supplementary Material

Supplemental Table 1. Summary of different proposed analytical IMF forms. Notation: lm = log₁₀(m/M) = ln(m/M)/ln10; dN is the number of single stars in the mass interval m to m+dm and in the logarithmic-mass interval lm to lm+dlm. The mass-dependent IMF indices, (m) (eq. ind), are plotted in Fig. 5 using the line-types defined here. Eq. MS was derived by Miller and Scalo assuming a constant star-formation rate and a Galactic disk age of 12 Ga (the uncertainty of which is indicated in the lower panel of Fig. 5A). Larson (76) does not fit his forms (eqs. La and Lb) to solar-neighborhood star-count data but rather uses these to discuss general aspects of likely systematic IMF evolution; the m_o in Eq. La and Lb given here are approximate eye-ball fits to the average IMF. In the multi-power-law IMF, ₃ = 2.3 is consistent with the data (Fig. 5), but correction for unresolved binary systems increases this to ₃ = 2.7. The uncertainties correspond to a 99% confidence interval for m > 0.5 M (Fig. 5), and to a 95% confidence interval for 0.1-0.5 M (12). The nearby Hipparcos LF, _near(Hipp) (Fig. 1), has = (5.9 ± 0.3) × 10^-3 stars/pc³ in the interval M_V = 5.5-7.5 corresponding to the mass interval m₂ = 0.891 -0.687 M (40) using the KTG93 MLR (Fig. 2). _m1^m₂(m) dm = yields k = 0.877 ± 0.045 stars/(pc³ M).

Medium version | Full size version

---

Supplemental Table 2. The number fraction is _N = 100 _m1^m₂(m) dm/ _ml^m_u(m) dm. The mass fraction is _M = 100 _m1^m₂ m (m) dm/ M_cl, M_cl = _ml^m_u m (m) dm. Both are in percent for main-sequence stars in mass intervals m₁ to m₂. The stellar contribution to the Oort limit, ^st, and to the Galactic-disk surface mass-density, ^st = 2 h^st. The above quantities assume for the lower and upper mass limits, respectively, m_l = 0.01 M and m_u = 120 M. The Galactic-disk scale-height h = 250 pc for m < 1 M (12) and h = 90 pc for m > 1 M (10). Results are shown for the average IMF (eq. 5 in Web table 1), for the high-mass-star IMF approximately corrected for unresolved companions (₃ = 2.7, m > 1 M), and for the PDMF in the solar neighborhood [₃ = 4.5 (10, 12)] which describes the distribution of stellar masses now populating the Galactic disk. The ISM contributes ^ISM = 13 ± 3 M/pc², ^ISM 0.04 ± 0.02 M/pc³ and stellar remnants contribute ^rem 3 M/pc², ^rem 0.003 M/pc³ (120). BDs do not constitute a dynamically important mass component of the Galaxy, even when eq. 5 is extrapolated to 0.0 M giving ^BD = 3.3 × 10^-3 M/pc³. The average stellar mass is ?m = _ml^m_u m (m) dm/_ml^m_u(m) dm. N_cl is the number of stars that have to form in a star cluster so that the most massive star in the population has the mass m_max. The mass of this population is M_cl, and the condition is _mmax(m) dm = 1 with _0.01^m_max (m) dm = N_cl-1. M_cl/M_cl is the fraction of mass lost from the cluster due to stellar evolution, assuming that for m 8 M all neutron stars and black holes are kicked out due to an asymmetrical supernova explosion, but that white dwarfs are retained (121) and have masses m_WD = 0.7 M for progenitor masses 1 m/M < 8 and m_WD = 0.5 M for 0.7 m/M < 1. The evolution times for a star of mass m_to to reach the turn-off age are available in Fig. 5.

Medium version | Full size version

---

Supplemental Table 3. ( < lm > ) data obtained after 1998. The data are shown in Fig. 5A in addition to the previously available data set compiled by Scalo (117). Each value is obtained at < lm > = (lm2-lm1)/2, lm = log10m, by the respective authors by fitting a power-law MF over the logarithmic mass range given by m1 and m2 listed above. Some authors do not quote uncertainties on their values. Notes: * are starburst clusters; 1 thin green open circle emphasizes the low-mass M35 datum; 2 the mass range 1.35 < m/M < 2.1 may be incomplete and is emphasized by the cross through the cyan large open triangle.
	mass range [M]	mass range [M]	mass range [M]
Orion nebula cluster, ONC
Muench et al. (48)	-0.35	+1.25	+2.35
magenta small open circles with central dot	0.02-0.08	0.08-0.80	0.80-63.1
magenta large open circles with central dot	+0.00	+1.00	+2.00
	0.02-0.08	0.08-0.40	0.4-63.10
Hillenbrand & Carpenter (46) (HC00)	+0.43
magenta large thick open circle	0.02-0.15
with central dot
Luhman (47)	+0.70
magenta small thick open circle	0.035-0.56
with central dot
Pleiades
Moraux et al. (122)	+0.51±0.15
green circles with central dot	0.04-0.30
Hambly et al. (115), from (55)	+0.56	+2.67
green circles with central dot	0.065-0.60	0.6-10.0
Ori
Bejar et al. (57)	0.8±0.4
green solid circle	0.013-0.20
M35
Navascues et al. (55)	-0.88±0.12	0.81±0.02	2.59±0.04
green solid circle1	0.08-0.2	0.2-0.8	0.8-6.0
IC 348
Najita et al. (123) for MLR from (98)	+0.5
green solid circle	0.015-0.22
NGC 2264
Park et al. (124)			+2.7
green solid circle			2.0-6.3
5 LMC regions
Parker et al. (125)			+2.3±0.2
blue solid triangle			5-60
NGC 1818 in LMC
Santiago et al. (126), outer region		+2.5
blue solid triangle		0.9-3
NGC 1805 in LMC
Santiago et al. (126), outer region		+3.4
blue solid triangle		0.9-3
30 Dor* in LMC
Selman et al. (127), r > 3.6 pc			+2.37±0.08
cyan small open triangle			3-120
Selman et al. (127), 1.1 < r/pc < 4.5			+2.17±0.05
cyan small open triangle			2.8-120
Sirianni et al. (68)		+1.27±0.08	+2.28±0.05
cyan large open triangle2		1.35-2.1	2.1-6.5
Arches cluster*
Figer et al. (128), all radii			+1.6±0.1
cyan large solid circle			6.3-125
NGC 3603*
Eisenhauer et al. (129)		+1.73	+2.7
cyan small solid circle		1-30	15-70
Globular clusters
Piotto & Zoccali (50)	+0.88±0.35	+2.3
yellow open triangles	0.1-0.6	0.6-0.8
Galactic bulge
Holtzman et al. (38)	+0.9	+2.2
magenta filled square	0.3-0.7	0.7-1.0
Zoccali et al. (131)	+1.43±0.13	+2.0±0.23
magenta filled square	0.15-0.5	0.5-1.0
Solar Neighborhood (magenta dotted lines)
Reid et al. (132)	+1.5±0.5
	0.02-0.08
Herbst et al. (130)	+0.8
	0.02-0.08
Chabrier (15, 119)	+1	+1 / +2
	0.01-0.08	0.10-0.35 / 0.35-1.0

---

WEB REFERENCES

(numbering continued from printed paper).
119. G. Chabrier, Astrophys. J. 554, 1274 (2001). 120. V. Weidemann, in Baryonic Dark Matter, D. Lynden-Bell, G. Gilmore, Eds. (Kluwer Academic, Dordrecht, Netherlands, 1990), pp. 87.
121. V. Weidemann et al., Astron. J. 104, 187 (1992).
122. E. Moraux, J. Bouvier, J. R. Stauffer, Astron. Astrophys. 367, 211 (2001).
123. J. R. Najita, G. P. Tiede, J. S. Carr, Astrophys. J. 541, 977 (2000).
124. B.-G. Park et al., Astron. J. 120, 894 (2000).
125. J. Wm. Parker et al., Astron. J. 121, 891 (2001).
126. B. Santiago et al., Astron. Astrophys. 369, 74 (2001).
127. F. Selman et al., Astron. Astrophys. 347, 532 (1999).
128. D. F. Figer et al., Astrophys. J. 525, 750 (1999).
129. F. Eisenhauer et al., Astrophys. J. 498, 278 (1998).
130. T. M. Herbst et al., Astrophys. J. 526, L17 (1999).
131. M. Zoccali et al., Astrophys. J. 530, 418 (2000).
132. N. Reid et al., Astrophys. J. 521, 613 (1999).