\begin{table}%t5 \caption{\label{Istars-table-Prot}Gyrochronological ages for I-sequence stars in M~34.} %\centering \par \begin{tabular}{clccllll} \hline\hline \noalign{\smallskip} Identifier & ~~~JP\tablefootmark{a} & $\#$ of & $(B-V)_{o}$ & ~Measured & ~~Gyro Age\tablefootmark{c} & Fitted\tablefootmark{d} & Period\tablefootmark{e} \\ & ~~~ No. & periods & & ~~~Period & & Period & Variance \\ & & derived\tablefootmark{b} & & ~~~~[days] & ~~~~~[Myr] & [days] & [days$^{2}$] \\ \hline F4\_0136 & JP 213 & 2 & 0.544 & $ 2.87 \pm 0.03$ & $178.5 \pm 3.5$ & ~2.99 & 0.0144 \\ F4\_0169 & JP 50 & 4 & 0.598 & $ 3.81 \pm 0.08$ & $170.0 \pm 6.7$ & ~4.08 & 0.0729 \\ F4\_0234 & JP 148 & 3 & 0.698 & $ 5.56 \pm 0.07$ & $188.4 \pm 4.4$ & ~5.63 & 0.0049 \\ F4\_0303 & JP 227 & 4 & 0.767 & $ 7.4 \pm 0.3$ & $244.1 \pm 18.6$ & ~6.5 & 0.81 \\ F4\_0317 & JP 224 & 4 & 0.805 & $ 6.8 \pm 0.1$ & $183.8 \pm 5.0$ & ~7.0 & 0.04 \\ F4\_0327 & JP 199 & 2 & 0.813 & $ 7.6 \pm 1.1$ & $220.9 \pm 59.8$ & ~7.1 & 0.25 \\ F3\_0172 & JP 49 & 3 & 0.811 & $ 8.0 \pm 1.0$ & $244.6 \pm 57.2$ & ~7.0 & 1.00 \\ F3\_0215 & JP 41 & 4 & 0.874 & $ 7.47 \pm 0.11$ & $180.4 \pm 5.0$ & ~7.74 & 0.0729 \\ F4\_0450 & JP 113 & 4 & 0.895 & $ 8.00 \pm 0.21$ & $194.5 \pm 9.6$ & ~7.96 & 0.0016 \\ F3\_0258 & JP 289 & 3 & 0.947 & $11.0 \pm 1.0$ & $313.1 \pm 53.3$ & ~8.5 & 6.25 \\ F4\_0667 & JP 52 & 3 & 1.030 & $ 7.97 \pm 0.05$ & $145.0 \pm 1.7$ & ~9.28 & 1.7161 \\ F3\_0320 & JP 172 & 3 & 1.046 & $ 8.511 \pm 0.001$ & $159.3 \pm 0.1$ & ~9.429 & 0.84272 \\ F4\_0730 & JP 18 & 4 & 1.051 & $ 8.41 \pm 0.10$ & $154.4 \pm 3.4$ & ~9.47 & 1.1236 \\ F3\_0383 & & 2 & 1.160 & $ 9.5 \pm 0.4$ & $162.2 \pm 12.8$ & 10.4 & 0.81 \\ F4\_0803 & JP 229 & 2 & 1.164 & $12.6 \pm 0.7$ & $273.5 \pm 28.5$ & 10.5 & 4.41 \\ F4\_0942 & & 3 & 1.198 & $ 9.4 \pm 0.3$ & $150.4 \pm 9.0$ & 10.7 & 1.69 \\ F3\_0430 & & 1 & 1.239 & $10.5 \pm 1.0$ & $174.8 \pm 31.2$ & 11.1 & 0.36 \\ F3\_0485 & & 2 & 1.285 & $12.0 \pm 1.0$ & $211.3 \pm 33.0$ & 11.4 & 0.36 \\ F3\_0469 & & 4 & 1.283 & $12.9 \pm 0.3$ & $242.5 \pm 10.6$ & 11.4 & 2.25 \\ F4\_1315 & & 2 & 1.371 & $12.2 \pm 0.5$ & $196.4 \pm 15.1$ & 12.1 & 0.01 \\ F4\_1357 & & 2 & 1.380 & $ 9.4 \pm 0.2$ & $119.3 \pm 4.8$ & 12.2 & 7.84 \\ F3\_0664 & & 1 & 1.441 & $10.5 \pm 1.0$ & $137.2 \pm 24.5$ & 12.6 & 4.41 \\ F4\_1369 & & 2 & 1.443 & $11.85 \pm 0.13$ & $171.7 \pm 3.5$ & 12.61 & 0.5776 \\ F4\_1566 & & 2 & 1.479 & $11.2 \pm 0.1$ & $148.8 \pm 2.5$ & 12.9 & 2.89 \\ F4\_1007 & & 2 & 1.440 & $15.0 \pm 2.0$ & $267.8 \pm 66.8$ & 12.6 & 5.76 \\ F4\_1925 & & 1 & 1.507 & $12.7 \pm 2.0$ & $183.0 \pm 53.9$ & 13.1 & 0.16 \\ \hline \end{tabular} \tablefoot {\tablefoottext{a}{{\em JP} identifier from Jones \& Prosser (\cite{Jone96}).} \\ \tablefoottext{b}{Number of filter/exposure combinations yielding photometric period derivations for a given star.} \\ \tablefoottext{c}{Gyro ages determined using Meibom et~al. (\cite{Meibo09}) I-sequence colour function coefficients, {\em viz} $a=0.770$~$\pm$ $0.014$, $b=0.553$~$\pm$ $0.052$ and $c=0.472$~$\pm$ $0.027$, and an age function exponent $n=0.5344$~$\pm$ $0.0015$ (see Sect.~\ref{M34gyro}).} \\ \tablefoottext{d}{Assuming a mean gyrochronology age for M~34 of 193~Myr (the~mean of the ages calculated in Col.~6~-- see Sect.~\ref{M34gyro}) and the Meibom et~al. (\cite{Meibo09}) coefficients, with $n=0.5344$~$\pm$ $0.0015$, we use intrinsic ($B-V$)~colours and Eq.~(1) to derive a fitted period for each M~34 I-sequence star.} \\ \tablefoottext{e}{Each star's contribution to the period variance [(Measured Period~-- Fitted Period)$^{2}$] is noted, where the total variance is 43.73~days${^2}$, with a mean of 1.68~days${^2}$.}} \end{table}