The Initial Core Mass Function Near and Far Su Yu-Nung ASIAA Liu, Sheng-Yuan Chen, Vivien The 5th ALMA J-T Science Workshop Alves et al. 2007 NTHU, Hsinchu December 5-6, 2008
Outline • Background & Motivation – Initial mass function – Core mass function • Observational Strategy – Required sensitivity – Frequency: low or high ? – Targets: near or far ? – Other concerns • Summary
Background - IMF • Initial Mass Function – A series of power-law form of stellar population dN/dM ~ M - α α = 2.35 – 2.7 for star mass > 0.6-1 M ⊙ (Salpeter 1955, Miller & Scalo 1979, Kroupa 2002, Muench et al. 2002) – Nevertheless, the origin the stellar IMF remains one of the major unsolved problems in modern astrophysics. – Since stars form in molecular clouds, the knowledge of mass spectrum of molecular cloud cores is likely a key for understanding the origin of the IMF
Background - CMF • Core Mass Function – Observations of nearby star forming regions • mm/sub-mm dust continuum – Serpens, Testi & Sargent 1998 – Orion A, Johnstone & Bally 1999, 2006 – Orion B, Johnstone et al. 2001, 2006 – ρ Ophiuchus, Motte et al. 1998, Johnstone et al. 2000 – NGC 2068/2071, Motte et al. 2001 • molecular line emission – nearby clouds, C 18 O, Tachihara et al. 2002 – Taurus, H 13 CO + , Onishi et al. 2002 – Orion A, H 13 CO + , Ikeda et al. 2007 • near-IR extinction – Pipe dark cloud, Alves et al. 2007
Background - CMF The dense core mass function derived from near-IR extinction map in the Pipe dark cloud (Alves et al. 2007) • 159 dense cores identified • the DCMF is similar in shape to the IMF • but shifted by a factor of 3 to higher masses • IMF is the direct product of the dense core mass function • A uniform star formation efficiency of ~ 30%
Background - CMF Similar power indices have been identified by mm/sub-mm continuum as well as molecular line surveys The location of the break is similar to that of IMF (Motte et al. 1998; 2001) Incompleteness sample at low-mass end (Testi et al. 1998, Johnstone et al. 2001) Lack of identification of “massive cores” (Motte et al. 2001) NGC 2068/2071 Pipe dark cloud Serpen Testi & Sargent 1998 Motte et al. 2001 (Alves et al. 2007)
Similar DRSP The Connection Between Cloud Structure and the IMF C. Chandler, A. Wootten, J. Mangum Science goal: The origin of the IMF and its relationship to the initial conditions within star forming molecular clouds is one of the major unsolved problems in star formation, and one which has implications for almost every scientific field in which ALMA will be important. We propose to conduct a large-scale survey of the Ophiuchus, Lupus, Perseus, and Orion molecular cloud complexes in order to determine this relationship. The main survey will be carried out at 1 mm, and companion survey at 3 mm is needed to enable us to distinguish unambiguously between dust and free-free emission. Number of sources: 4 (Ophiuchus, Perseus, Lupus, and Orion) Total integration time: 400 hrs
Similar DRSP 5. Spatial scales: 5.1. Angular resolution: 1" 5.2. Range of spatial scales/FOV: 1 degree 5.3. Single dish: yes 5.4. ACA: yes 5.5. Subarrays: no 6. Frequencies: 6.1. Receiver band: Band 6 230 GHz and Band 3 100 GHz 7. Continuum flux density: 7.1. Typical value: 1 mJy 7.2. Continuum peak value: 1 Jy 7.3. Required continuum rms: 0.3 mJy 7.4. Dynamic range in image: 1000 10. Integration time per setting: 4 x 6 s x 57600 fields at 230 GHz 4 x 1 s x 14400 fields at 100 GHz (NOTE: use OTF mosaicing)
Proposed Observations • Can ALMA do such kind of survey ? • What is the required total integration time ? – Cloud @ 2kpc – 6 pc x 3 pc (comparable to OMC 1,2,3, and 4) – 600’’ x 300’’ – Observations 230 GHz – Rms 0.54 mJy (= 5 sigma mass detection for 0.3 M ☉ sources) – Total integration time : 38 mins (2.15 s x 1050 field) (http://www.eso.org/sci/facilities/alma/observing/tools/etc/index.html) • Are observations at 230 GHz band the best choice ?? (in terms of sensitivity, resolution…)
Observations: high freq. or low freq. For the same rms (in terms of Jy), the integration time ratio ~ 1 : 5 : 20 : 170 for observations at 100, 230, 345, and 690 GHz) � high-freq. is slow Field number ∝ ν 2 � high freq. will be even slow Observations at 650 GHz band are much slower than that at 100 GHz band!! III IV V VI VII VIII IX Observations at 3-mm are fastest
Observations: high freq. or low freq. But for obs. at different frequency, the required rms noise levels are not same. What we need is the same mass detection limit . for β =0, flux ~ ν 2 rms ~ ν 2 integration time ~ ν -4 Obs @ 230 GHz is the most efficient, but only a factor of 5 faster than obs @ 650 band !!
Observations: high freq. or low freq. for β =0.5, rms ~ ν 2.5 integration time ~ ν -5 for β =1.0, rms ~ ν 3 integration time ~ ν -6 High-freq is better !! For β =1.0, obs @ 650 band is the fastest
Observations: high freq. or low freq. for β =1.5, rms ~ ν 3.5 integration time ~ ν -7 for β =2.0, rms ~ ν 4 integration time ~ ν -8 for β =2, observations @ 680 GHz, the required total integration time is only 2 mins !! (2kpc, 6 pc x 3 pc, 5 sigma detection limit of 0.3 M ⊙ sources)
Source Selection Distant or Nearby ?? single field: for the same mass detection limit (F ~ M/d 2 ) rms noise level ~ 1/d 2 integration time ~ d 4 Field Number for the same physical area filed number ~ d -2 Nearer is faster Total integration time ~ d 2 2 kpc : 2 mins (0.014 s / field) 20 kpc : 200 mins (137 s / field) 50 kpc : 1250 mins = 21 hrs (90 m / field)
Observations Are observations at 680 GHz really the best choice ? – Resolution, largest and smallest scales ?? – Can we have such a “short” integration time ?? • Sub-array mode ?? • OTF mode ?? • target even low-mass objects (0.1 M ⊙ ??) – Dynamical Range ?? • 0.3 M ⊙ to a few tens M ⊙ • > 200 • more data toward luminous sources ?? – Given large mosaic fields, can we obtain “uniform” map ??
Resolution and uv Coverage Aboved-mention conclusions (i.e., 680 GHz is the fastest, and nearer is faster) are based on the assumption of point-like structure. Such assumption, however, may not be valid Dense core size : 2,000 – 10,000 AU � 1”-5” @ 2kpc (Motte et al. 1998, 2001) Band frequency angular resolution line continuum primary largest range b max =200m ... 18km sensitivity sensitivity beam scale (GHz) (arcsec) (mJy) (mJy) (arcsec) (arcsec) For sources at 2 kpc, even the most compact one will 3 84-116 3.0 ... 0.034 8.9 0.060 56 37 be resolved with ALMA observations at high-freq. 4 125-169 2.1 ... 0.023 9.1 0.070 48 32 (>400 GHz) bands 5 163-211 1.6 ... 0.018 150 1.3 35 23 6 211-275 1.3 ... 0.014 13 0.14 27 18 7 275-373 1.0 ... 0.011 21 0.25 18 12 8 385-500 0.7 ... 0.008 63 0.86 12 9 9 602-720 0.5 ... 0.005 80 1.3 9 6 http://www.eso.org/sci/facilities/alma/observing/specifications/
Resolution and uv Coverage For sources at distance > 4kpc, the two conclusions are likely valid if the less massive sources have smaller sizes Although the brighter sources 10000 AU can be well resolved, sensitivity is unlikely an issue 2000 AU if applying taper weighting Assuming uniform uv coverage (visibility number / uv area ~ const) Rms ~ beam size using uv < 0.1 x bmax beam size � x 10 rms � x 10 mass limit � x 10
Summary for Clouds with d > 4 kpc For sources at distance > 4 kpc, observations @ 680 GHz are the most efficient. The required integration time for a single field : β =1 1.92 x (d/4kpc) 4 sec β =2 0.22 x (d/4kpc) 4 sec Total integration time: (6 pc x 3 pc, field number~ 2200 (d/4kpc) -2 ) 70 x (d/4kpc) 2 min β =1 8 x (d/4kpc) 2 min β =2
Resolution and uv Coverage For sources located within 4 kpc, we have to reexamine the two conclusions. (i.e., 680 GHz is the fastest, and nearer is faster) 1. If the sources are well resolved, what is the relationship between integration time and source distance ? for sources with the same mass total flux ~ d -2 + source angular size ~ d -1 � constant brightness � required rms level not related to distance but for mapping the same physical scale, mosaic field number ~ d -2 � farther is faster !!
Resolution and uv Coverage For sources with d < 4 kpc, we have to reexamine the two conclusions. (i.e., 680 GHz is the fastest, and nearer is faster) 4 kpc, 0.5”, 5 mJy, rms 1mJy � 5 simga 1. If the sources are well resolved, what is the relationship between 2 kpc, 1’’, 20 mJy integration time and source distance ? resolution 0.5”, rms 2mJy taper � 1.0”, rms 4 mJy � 5 simga for sources with the same mass 1 kpc, 2’’, 80 mJy total flux ~ d -2 resolution 0.5”, rms 4mJy taper � 2.0”, rms 16 mJy � 5 sigma source angular size ~ d -1 if applying taper weighting � rms ~ d -1 � integration time ~ d 2 � but field number ~ d -2 farther is faster !! � total integration time cont. over source distance
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