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I was reading this paper on the ejecta mass of compact binary mergers and came across this notation in equation (6):

$$\frac{M_\text{dyn}}{10^{-3}M_\odot}=\left(\frac{a}{C_1}+b\frac{M_2^n}{M_1^n}+cC_1\right)M_1+(1\leftrightarrow 2)$$

which is an equation of the dynamical ejecta mass of a binary neutron star merger in terms of the mass and compactness of the two neutron stars with coefficients $a,b,c,d$ fitted to simulations. My question is what does the notation $(1 \leftrightarrow 2)$ mean in this context?

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    $\begingroup$ Could be a sloppy way of writing "a number between 1 and 2". Do they reference other papers where this is coming from? $\endgroup$
    – AtmosphericPrisonEscape
    Feb 28 at 17:34
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    $\begingroup$ @AtmosphericPrisonEscape This is the paper being referenced but I don't think it contains a clarification either. $\endgroup$
    – hikari30
    Feb 28 at 19:05
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    $\begingroup$ @AtmosphericPrisonEscape Sorry, I just realized I did not include the actual link. Here's the link to the paper: arxiv.org/pdf/1612.03665.pdf $\endgroup$
    – hikari30
    Mar 1 at 3:47
  • $\begingroup$ You cross-posted this on Physics SE, where you also got an answer. Could you please close this question so it is not left as an unanswered question on the system. In general cross-posting is discouraged. $\endgroup$
    – StephenG - Help Ukraine
    Mar 2 at 0:49
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    $\begingroup$ I'd suggest you copy the answer from Physics SE and put it here. You can accept than answer as well and it will remove an unanswered question from the system. In case you're wondering there is no problem with self-answering questions on SE. $\endgroup$
    – StephenG - Help Ukraine
    Mar 2 at 11:43

1 Answer 1

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This work deals about binary mergers, i.e. two stars with (different) gravitational masses $M_1$ and $M_2$ and accordingly two different compactness $C_1$ and $C_2$, see below Eq.(4) for more details.

The meaning of the arrow in Eq.(6) is simply copy the complete previous (left) expression and replace any index 1 by 2 and vice versa. Thus, the second summand reads written out in detail $$ \ldots + \left( \frac{a}{C_2} + b \frac{M^n_1}{M^n_2} +cC_2\right) M_2 $$

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