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Set $s=0$ in the horizontal-field magnetoconvection dispersion relation. With positive $\sigma ,\zeta$ and nonzero $a_h$, cancellation gives the stationary neutral curveAt fixed $a_h^2$, the Chandrasekhar number contributes a nonnegative penalty proportional to $m^2$. It can be eliminated by choosing $m=0$. It remains to minimize $f(x)=(x+{\pi }^2{)}^3/x$ for $x=k^2>0$:The function diverges at both endpoints and has its unique minimum at $x={\pi }^2/2$. Thus the magnetic-field-aligned rolls evade steady magnetic inhibition:independently of $Q$. If higher vertical sine modes are included, replacing $\pi$ by $n\pi$ gives minimum $27n^4{\pi }^4/4$, so the displayed first vertical mode also gives the smallest steady threshold.

Physically, these convection rolls have axes along the imposed magnetic field. Their perturbations are independent of $y$, so ${\partial }_y\mathbf{u}=0$ in the resistive induction equation and no growing magnetic perturbation is generated. The flow does not bend the field; consequently magnetic tension cannot inhibit these rolls, however large the field strength. This conclusion concerns the requested steady disturbances.