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              <p>ABSTRACT Numerical simulations predict that clumps ($\sim$1 pc) should form stars at high efficiency to produce bound star clusters. We conducted a statistical study of 17 nearby cluster-forming clumps to examine the star formation rate and gas mass surface density relations (i.e. $\Sigma _{\rm {SFR}}$ versus $\Sigma _{\rm {gas}}$) at the clump scale. Using near-infrared point sources and ${\it Herschel}$ dust continuum analysis, we obtained the radius, age, and stellar mass for most clusters in the ranges 0.5–1.6 pc, 0.5–1.5 Myr, 40–500 M$_{\odot }$, respectively, and also found that they are associated with $\Sigma _{\rm {gas}}$ values ranging from 80 to 600 M$_{\odot }$ pc$^{-2}$. We obtained the best-fitting scaling relations as $\Sigma _{\rm {SFR}}$ $\propto$ $\Sigma _{\rm {gas}}^{1.46}$ and $\Sigma _{\rm {SFR}}$ $\propto$ $(\Sigma _{\rm {gas}}/t_{\rm {ff}})^{0.80}$ for the studied sample of clumps. Comparing our results with existing scaling relations at cloud and extragalactic scales, we found that while the power-law exponent obtained in this work is similar to those found at these scales, the star formation rate surface densities are relatively higher for similar gas mass surface densities. From this work, we obtained instantaneous median star formation efficiency (SFE) and efficiency per free-fall time ($\epsilon _{\rm {ff}}$) of $\sim$20 per cent and $\sim$13 per cent, respectively, for the studied clumps. We discuss the cause of the obtained high SFE and $\epsilon _{\rm {ff}}$ in the studied clumps and also discuss the results in the context of bound cluster formation within molecular clouds. We conclude that our results do not favour a universal scaling law with a constant value of $\epsilon _{\rm {ff}}$ in star-forming systems across different scales.</p>
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        <org type="institution" xml:id="struct-307314" status="VALID">
          <orgName>Centre National d'Études Spatiales [Toulouse]</orgName>
          <orgName type="acronym">CNES</orgName>
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            <address>
              <addrLine>18 avenue Edouard Belin 31401 Toulouse</addrLine>
              <country key="FR"/>
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          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
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            <address>
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        <org type="institution" xml:id="struct-301855" status="VALID">
          <orgName>Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche</orgName>
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              <addrLine>1 rue Descartes - 75231 Paris cedex 05</addrLine>
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          <orgName>Université de Bordeaux</orgName>
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              <addrLine>35, place Pey Berland - 33076 Bordeaux</addrLine>
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        <org type="institution" xml:id="struct-452453" status="VALID">
          <idno type="ROR">https://ror.org/02gh4kt33</idno>
          <orgName>Istituto Nazionale di Astrofisica [Rome]</orgName>
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              <addrLine>Viale del Parco Mellini 84, 00136 Roma</addrLine>
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        <org type="institution" xml:id="struct-300884" status="VALID">
          <idno type="ROR">https://ror.org/02v51f717</idno>
          <orgName>Peking University [Beijing]</orgName>
          <desc>
            <address>
              <addrLine>No.5 Yiheyuan Road Haidian District, Beijing, P.R.China 100871</addrLine>
              <country key="CN"/>
            </address>
            <ref type="url">http://english.pku.edu.cn/</ref>
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</TEI>