The Stellar Mass versus Stellar Metallicity Relation of Star-forming Galaxies at 1.6 ≤ z ≤ 3.0 and Implications for the Evolution of the α-enhancement

<jats:title>Abstract</jats:title> <jats:p>We measure the relationship between stellar mass and stellar metallicity for 1336 star-forming galaxies at 1.6 ≤ <jats:italic>z</jats:italic> ≤ 3.0 using rest-frame far-ultraviolet spectra from the zCOSMOS-deep survey. High signal-to-noise ratio composite spectra containing stellar absorption features are fit with stellar population synthesis model spectra of a range of stellar metallicity. We find stellar metallicities, which mostly reflect instantaneous iron abundances, scaling as <jats:inline-formula> <jats:tex-math> <?CDATA $[\mathrm{Fe}/{\rm{H}}]=-(0.81\pm 0.01)+(0.32+0.03)\mathrm{log}({M}_{* }/{10}^{10}{M}_{\odot })$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">[</mml:mo> <mml:mi>Fe</mml:mi> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> <mml:mo stretchy="false">]</mml:mo> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0.81</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.01</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo>+</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0.32</mml:mn> <mml:mo>+</mml:mo> <mml:mn>0.03</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mi>log</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> </mml:msup> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac399eieqn1.gif" xlink:type="simple" /> </jats:inline-formula> across the stellar mass range of 10<jats:sup>9</jats:sup> ≲ <jats:italic>M</jats:italic> <jats:sub>*</jats:sub>/<jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub> ≲ 10<jats:sup>11</jats:sup>. The instantaneous oxygen-to-iron ratio (<jats:italic>α</jats:italic>-enhancement) inferred using the gas-phase mass–metallicity relation is on average found to be <jats:inline-formula> <jats:tex-math> <?CDATA $\left[{\rm{O}}/\mathrm{Fe}\right]\approx 0.47$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close="]" open="["> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>Fe</mml:mi> </mml:mrow> </mml:mfenced> <mml:mo>≈</mml:mo> <mml:mn>0.47</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac399eieqn2.gif" xlink:type="simple" /> </jats:inline-formula>, being higher than the local <jats:inline-formula> <jats:tex-math> <?CDATA $\left[{\rm{O}}/\mathrm{Fe}\right]\approx 0$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close="]" open="["> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>Fe</mml:mi> </mml:mrow> </mml:mfenced> <mml:mo>≈</mml:mo> <mml:mn>0</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac399eieqn3.gif" xlink:type="simple" /> </jats:inline-formula>. The observed changes in [O/Fe] and [Fe/H] are reproduced in simple gas-regulator models with steady star formation histories. Our models show that the [O/Fe] is determined almost entirely by the instantaneous specific star formation rate alone while being independent of the mass and the characteristic of the gas regulation. We also find that the locations of ∼ 10<jats:sup>10</jats:sup> <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub> galaxies at <jats:italic>z</jats:italic> ∼ 2 in the [O/Fe]–metallicity planes are in remarkable agreement with the sequence of low-metallicity thick-disk stars in our own Galaxy. This manifests a beautiful concordance between the results of Galactic archeology and observations of high-redshift Milky Way progenitors. There remains, however, a question of how and when the old metal-rich, low <jats:italic>α</jats:italic>/Fe stars seen in the bulge had formed by <jats:italic>z</jats:italic> ∼ 2 because such a stellar population is not seen in our data and is difficult to explain in the context of our models.</jats:p>