On the Zero Point Constant of the Bolometric Correction Scale

TL;DR

This paper clarifies the zero point constant of the bolometric correction scale, showing it is a definite positive value and that bolometric corrections are not always negative, contrary to common assumptions.

Contribution

It demonstrates that the zero point constant of the $BC_V$ scale is fixed and positive, challenging the traditional view that bolometric corrections must always be negative.

Findings

The zero point constant $C_2$ of $BC_V$ is positive and fixed.

Bolometric corrections are not necessarily negative.

Clarifies misconceptions about bolometric correction signs.

Abstract

Arbitrariness attributed to the zero point constant of the $V$ band bolometric corrections ($BC_V$) and its relation to "bolometric magnitude of a star ought to be brighter than its visual magnitude" and "bolometric corrections must always be negative" was investigated. The falsehood of the second assertion became noticeable to us after IAU 2015 General Assembly Resolution B2, where the zero point constant of bolometric magnitude scale was decided to have a definite value $C_{Bol}(W)= 71.197~425~...$~. Since the zero point constant of the $BC_V$ scale could be written as $C_2=C_{Bol}-C_V$, where $C_V$ is the zero point constant of the visual magnitudes in the basic definition $BC_V=M_{Bol}-M_V=m_{bol}-m_V$, and $C_{Bol}>C_V$, the zero point constant ($C_2$) of the $BC_V$ scale cannot be arbitrary anymore; rather, it must be a definite positive number obtained from the two definite positive numbers. The two conditions $C_2>0$ and $0<BC_V<C_2$ are also sufficient for $L_V<L$, a similar case to negative $BC_V$ numbers, which means that "bolometric corrections are not always negative". In sum it becomes apparent that the first assertion is misleading causing one to understand bolometric corrections must always be negative, which is not necessarily true.