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On the Common Envelope Efficiency
In this work, we try to use the apparent luminosity versus displacement
(i.e., vs. ) correlation of high mass X-ray binaries (HMXBs) to
constrain the common envelope (CE) efficiency , which is a key
parameter affecting the evolution of the binary orbit during the CE phase. The
major updates that crucial for the CE evolution include a variable
parameter and a new CE criterion for Hertzsprung gap donor stars, both of which
are recently developed. We find that, within the framework of the standard
energy formula for CE and core definition at mass \%, a high value of
, i.e., around 0.8-1.0, is more preferable, while likely can not reconstruct the observed vs.
distribution. However due to an ambiguous definition for the core boundary in
the literature, the used here still carries almost two order of
magnitude uncertainty, which may translate directly to the expected value of
. We present the detailed components of current HMXBs and
their spatial offsets from star clusters, which may be further testified by
future observations of HMXB populations in nearby star-forming galaxies.Comment: 14 pages, 10 figures, 7 tables, accepted for publication in MNRA
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