The Alpha Magnetic Spectrometer (AMS) on the International Space Station: Part II - Results from the First Seven Years

The positron flux $\Phi_{e^+}$ as a function of the energy $E$ at the top of AMS in units of $[{\rm m}^2 \, {\rm sr} \, {\rm s} \, {\rm GeV}]^{-1}$. Characteristic energy $\widetilde E$ (i.e. spectrally weighted mean energy in the bin) is given with its systematic error from the energy scale uncertainty. The number of positron events before unfolding, $N_{e^+}$ , is given together with its statistical error from the fit. $\sigma_{\rm stat}$ is the statistical error. $\sigma_{\rm syst}^{\rm tmpl}$ is the systematic error from the definition of templates. $\sigma_{\rm syst}^{\rm c.c.}$ is the systematic error from the charge confusion. $\sigma_{\rm syst}^{\rm eff}$ is the systematic error from the efficiency corrections. $\sigma_{\rm syst}^{\rm unf}$ is the systematic error from the unfolding. $\sigma_{\rm syst}$ is the total systematic error, which is equal to the sum of $\sigma_{\rm syst}^{\rm tmpl}$, $\sigma_{\rm syst}^{\rm c.c.}$, $\sigma_{\rm syst}^{\rm eff}$, and $\sigma_{\rm syst}^{\rm unf}$ in quadrature. $\sigma_{\rm syst}^{\rm eff}$ includes the correlated systematic error on the flux normalization of 1%. Note that this 1% error is subtracted in quadrature from the total systematic error for all the fits to the positron data in this Report.

The electron flux $\Phi_{e^-}$ as a function of the energy $E$ at the top of AMS in units of $[{\rm m}^2 \, {\rm sr} \, {\rm s} \, {\rm GeV}]^{-1}$. Characteristic energy $\widetilde E$ (i.e. spectrally weighted mean energy in the bin) is given with its systematic error from the energy scale uncertainty. The number of electron events before unfolding, $N_{e^-}$, is given together with its statistical error from the fit. $\sigma_{\rm stat}^{e^-}$  is the statistical and $\sigma_{\rm syst}^{e^-}$ is the total systematic error of the electron flux. Similar to positrons (see Table 1), the correlated systematic error of 1% is subtracted in quadrature from the total systematic error for all the fits to the electron data in this Report.

The positron fraction (${\rm PF} = \Phi_{e^+} /(\Phi_{e^-} + \Phi_{e^+})$) as a function of the energy $E$ at the top of AMS. Characteristic energy $\widetilde E$ (i.e. spectrally weighted mean energy in the bin) is given with its systematic error from the energy scale uncertainty. PF are calculated from the positron and electron fluxes (Sections 2 and 3). $\sigma_{\rm stat}^{\rm PF}$ and $\sigma_{\rm syst}^{\rm PF}$ are the statistical error and the total systematic error of the positron fraction. The systematic errors of the positron fraction account for correlations related to the calculation of the acceptance.

The combined (electron + positron) flux $\Phi_{e^-+e^+}$ in units of $[{\rm m}^2 \, {\rm sr} \, {\rm s} \, {\rm GeV}]^{-1}$ as a function of the energy $E$ at the top of AMS. Characteristic energy $\widetilde E$ (i.e. spectrally weighted mean energy in the bin) is given with its systematic error from the energy scale uncertainty. $\sigma_{\rm stat}^{e^-+e^+}$ and $\sigma_{\rm syst}^{e^-+e^+}$ are the statistical error and the total systematic error of the combined (electron + positron) flux. The systematic errors account for correlations related to the calculation of the acceptance.

The Proton flux $\Phi_p$ as a function of rigidity at the top of AMS in units of $[{\rm m}^2 \, {\rm sr} \, {\rm s} \, {\rm GV}]^{-1}$ including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger and acceptance ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic error.

The $\bar p$ flux $\Phi_{\bar p}$ in units of $[{\rm m}^2 \, {\rm sr} \, {\rm s} \, {\rm GV}]^{-1}$ and the (${\bar p}/p$) flux ratio $\Phi_{\bar p}/\Phi_p$ as a function of absolute rigidity at the top of AMS. ${\tilde N}_{\bar p}$ is the number of antiprotons observed in each rigidity bin rounded to the nearest integer. $\sigma_{\rm stat}$ and $\sigma_{\rm syst}$ are the respective statistical and systematic errors.

The Helium flux $\Phi_{He}$ as a function of rigidity at the top of AMS in units of $[{\rm m}^2 \, {\rm sr} \, {\rm s} \, {\rm GV}]^{-1}$ including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic error.

The Carbon flux $\Phi_{C}$ as a function of rigidity at the top of AMS in units of $[{\rm m}^2 \, {\rm sr} \, {\rm s} \, {\rm GV}]^{-1}$ including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic error.

The Oxygen flux $\Phi_{O}$ as a function of rigidity at the top of AMS in units of $[{\rm m}^2 \, {\rm sr} \, {\rm s} \, {\rm GV}]^{-1}$ including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic error.

The helium to oxygen flux ratio He/O as a function of rigidity including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The statistical errors are the sum in quadrature of the ratios of helium and oxygen fluxes statistical errors to the corresponding flux values, multiplied by the flux ratio. The systematic errors from the background subtraction, the trigger, and the event reconstruction and selection are likewise added in quadrature. The correlations in the systematic errors from the uncertainty in nuclear interaction cross sections, the unfolding and the absolute rigidity scale between the helium and oxygen fluxes have been taken into account in calculating the corresponding systematic errors of the flux ratio. The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic uncertainty.

The carbon to oxygen flux ratio C/O as a function of rigidity including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The statistical errors are the sum in quadrature of the ratios of carbon and oxygen fluxes statistical errors to the corresponding flux values, multiplied by the flux ratio. The systematic errors from the background subtraction, the trigger, and the event reconstruction and selection are likewise added in quadrature. The correlations in the systematic errors from the uncertainty in nuclear interaction cross sections, the unfolding and the absolute rigidity scale between the carbon and oxygen fluxes have been taken into account in calculating the corresponding systematic errors of the flux ratio. The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic uncertainty.

The proton to helium flux ratio p/He as a function of rigidity including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The statistical errors are the sum in quadrature of the ratios of proton and helium fluxes statistical errors to the corresponding flux values, multiplied by the flux ratio. The systematic errors from the background subtraction, the trigger, and the event reconstruction and selection are likewise added in quadrature. The correlations in the systematic errors from the uncertainty in nuclear interaction cross sections, the unfolding and the absolute rigidity scale between the proton and helium fluxes have been taken into account in calculating the corresponding systematic errors of the flux ratio. The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic uncertainty.

The Lithium flux $\Phi_{Li}$ as a function of rigidity at the top of AMS in units of $[{\rm m}^2 \, {\rm sr} \, {\rm s} \, {\rm GV}]^{-1}$ including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic error.

The Beryllium flux $\Phi_{Be}$ as a function of rigidity at the top of AMS in units of $[{\rm m}^2 \, {\rm sr} \, {\rm s} \, {\rm GV}]^{-1}$ including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic error.

The Boron flux $\Phi_{B}$ as a function of rigidity at the top of AMS in units of $[{\rm m}^2 \, {\rm sr} \, {\rm s} \, {\rm GV}]^{-1}$ including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic error.

The lithium to carbon flux ratio Li/C as a function of rigidity including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The statistical errors are the sum in quadrature of the ratios of lithium and carbon fluxes statistical errors to the corresponding flux values, multiplied by the flux ratio. The systematic errors from the background subtraction, the trigger, and the event reconstruction and selection are likewise added in quadrature. The correlations in the systematic errors from the uncertainty in nuclear interaction cross sections, the unfolding and the absolute rigidity scale between the lithium and carbon fluxes have been taken into account in calculating the corresponding systematic errors of the flux ratio. The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic uncertainty.

The beryllium to carbon flux ratio Be/C as a function of rigidity including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The statistical errors are the sum in quadrature of the ratios of beryllium and carbon fluxes statistical errors to the corresponding flux values, multiplied by the flux ratio. The systematic errors from the background subtraction, the trigger, and the event reconstruction and selection are likewise added in quadrature. The correlations in the systematic errors from the uncertainty in nuclear interaction cross sections, the unfolding and the absolute rigidity scale between the beryllium and carbon fluxes have been taken into account in calculating the corresponding systematic errors of the flux ratio. The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic uncertainty.

The boron to carbon flux ratio B/C as a function of rigidity including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The statistical errors are the sum in quadrature of the ratios of boron and carbon fluxes statistical errors to the corresponding flux values, multiplied by the flux ratio. The systematic errors from the background subtraction, the trigger, and the event reconstruction and selection are likewise added in quadrature. The correlations in the systematic errors from the uncertainty in nuclear interaction cross sections, the unfolding and the absolute rigidity scale between the boron and carbon fluxes have been taken into account in calculating the corresponding systematic errors of the flux ratio. The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic uncertainty.

The lithium to oxigen flux ratio Li/O as a function of rigidity including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The statistical errors are the sum in quadrature of the ratios of lithium and oxigen fluxes statistical errors to the corresponding flux values, multiplied by the flux ratio. The systematic errors from the background subtraction, the trigger, and the event reconstruction and selection are likewise added in quadrature. The correlations in the systematic errors from the uncertainty in nuclear interaction cross sections, the unfolding and the absolute rigidity scale between the lithium and oxigen fluxes have been taken into account in calculating the corresponding systematic errors of the flux ratio. The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic uncertainty.

The beryllium to oxygen flux ratio Be/O as a function of rigidity including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The statistical errors are the sum in quadrature of the ratios of beryllium and oxygen fluxes statistical errors to the corresponding flux values, multiplied by the flux ratio. The systematic errors from the background subtraction, the trigger, and the event reconstruction and selection are likewise added in quadrature. The correlations in the systematic errors from the uncertainty in nuclear interaction cross sections, the unfolding and the absolute rigidity scale between the beryllium and oxygen fluxes have been taken into account in calculating the corresponding systematic errors of the flux ratio. The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic uncertainty.

The boron to oxygen flux ratio B/O as a function of rigidity including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The statistical errors are the sum in quadrature of the ratios of boron and oxygen fluxes statistical errors to the corresponding flux values, multiplied by the flux ratio. The systematic errors from the background subtraction, the trigger, and the event reconstruction and selection are likewise added in quadrature. The correlations in the systematic errors from the uncertainty in nuclear interaction cross sections, the unfolding and the absolute rigidity scale between the boron and oxygen fluxes have been taken into account in calculating the corresponding systematic errors of the flux ratio. The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic uncertainty.

The Nitrogen flux $\Phi_N$ as a function of rigidity at the top of AMS in units of $[{\rm m}^2 \, {\rm sr} \, {\rm s} \, {\rm GV}]^{-1}$ including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic error.

The nitrogen to oxygen flux ratio N/O as a function of rigidity including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The statistical errors are the sum in quadrature of the ratios of nitrogen and oxygen fluxes statistical errors to the corresponding flux values, multiplied by the flux ratio. The systematic errors from the background subtraction, the trigger, and the event reconstruction and selection are likewise added in quadrature. The correlations in the systematic errors from the uncertainty in nuclear interaction cross sections, the unfolding and the absolute rigidity scale between the nitrogen and oxygen fluxes have been taken into account in calculating the corresponding systematic errors of the flux ratio. The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic uncertainty.

The nitrogen to boron flux ratio N/B as a function of rigidity including errors due to statistics ($\sigma_{\rm stat}$); contributions to the systematic error from the trigger, acceptance, and background acceptance ($\sigma_{\rm acc}$); the rigidity resolution function and unfolding ($\sigma_{\rm unf}$); the absolute rigidity scale ($\sigma_{\rm scale}$); and the total systematic error ($\sigma_{\rm syst}$). The statistical errors are the sum in quadrature of the ratios of nitrogen and boron fluxes statistical errors to the corresponding flux values, multiplied by the flux ratio. The systematic errors from the background subtraction, the trigger, and the event reconstruction and selection are likewise added in quadrature. The correlations in the systematic errors from the uncertainty in nuclear interaction cross sections, the unfolding and the absolute rigidity scale between the nitrogen and boron fluxes have been taken into account in calculating the corresponding systematic errors of the flux ratio. The contribution of individual sources to the systematic error are added in quadrature to arrive at the total systematic uncertainty.