It's About Time:

It's About Time:

AMS antimatter data and cosmic ray propagation

Kfir Blum, IAS

Katz et al; MNRAS 405 (2010) 1458 KB; JCAP 1111 (2011) 037

KB, Katz, Waxman; PRL 111, 211101 (2013)

AMS Days at CERN 04/15/2015

Open questions:

What is the source of Galactic cosmic rays?

How do cosmic rays escape from the Galaxy?

Do we see exotic sources like dark matter or pulsars?

AMS data = major progress.

I will give my take on some of the AMS results, focusing on e+ and pbar.

Aim at what we can calculate and what we can learn, without committing to detailed model assumptions.

Antimatter occurs as secondary

Secondary CRs

•  Empirical relation:

•  = Local net production per unit column density of target, for species A

Stable secondaries with no energy loss (boron, pbar, sub-Fe,…)

A local account of secondary cosmic rays

Kfir Blum^1,⇤ and Kohta Murase^{1, †}

1Institute for Advanced Study, Princeton 08540, USA

We calculate the total production rate per unit volume of high energy (10-150 GeV) secondary positron and antiproton cosmic rays in the local interstellar medium, over distances of order 500pc from the Solar System. Comparing the net production rate to the locally observed cosmic ray densities, we deduce a confinement time of cosmic rays in the solar neighborhood, of order te ⇡?.

This calculation serves as a sanity test for the secondary origin of high energy cosmic ray antimatter.

The result is...

Introduction.

n_B(R, ~r , t ) = Z

d³r Z

dt c ⇢_ISM(~r, t) 2

4 X

i=C,N,O,...

⇣ _i

!B

¯ m

⌘n_i(R, ~r, t) ⇣ _B

¯ m

⌘n_B(R, ~r, t) 3

5 P (R; {~r, t}, {~r , t })

= 2

4 X

i=C,N,O,...

⇣ _i

!B

¯ m

⌘n_i(R, ~r , t ) ⇣ _B

¯ m

⌘n_B(R, ~r , t ) 3 5 Z

d³r Z

dt c ⇢_ISM(~r, t) n_C (R, ~r, t)

n_C (R, ~r , t ) P (R; {~r, t}, {~r , t }) F^B

⇡ Q^B(R) X^esc(R) (1)

Q_B(R) = X

i=C,N,O,...

⇣ _i

!B

¯ m

⌘n_i(R, ~r , t ) ⇣ _B

¯ m

⌘n_B(R, ~r , t ) (2)

Q_B(R, ~r, t) = X

i=C,N,O,...

⇣ _i

!B

¯ m

⌘n_i(R, ~r, t) ⇣ _B

¯ m

⌘n_B(R, ~r, t) (3)

X_esc = Z

d³r Z

dt c ⇢_ISM(~r, t) nC (R, ~r, t)

n_C (R, ~r , t ) P (R; {~r, t}, {~r , t }) (4)

FB =

P

i=C,N,O,... ⁱm^!B¯

ni(R,~r,t)

nC(R,~r,t) m¯^B

nB(R,~r,t) nC(R,~r,t)

P

i=C,N,O,... ⁱm^!B¯

ni(R,~r ,t )

nC(R,~r ,t ) m¯^B

nB(R,~r ,t ) nC(R,~r ,t )

⇡ 1 (5)

n_A(R)

n_B(R) = Q_A(R)

Q_B(R) (6)

n_A(R) = Q^A(R) ⇥ X^esc(R) (7)

Gamma ray observations provide evidence that the spectrum and density of CRs in the interstellar medium (ISM) on moderate distances (100-500pc) from the Solar System are approximately uniform, and consistent with the local measurements outside of the Earth’s atmosphere. Combining the locally measured CR flux with estimates of the mass of ISM gas in the solar neighborhood, we can therefore calculate the production rate of secondary CRs in this region.

This calculation is free of modeling assumptions for the distribution and propagation of CRs, that apply on larger spatial scales.

Comparing the calculated local net production rate of secondary CRs to their observed densities, we can infer the trapping time of the CRs in the local ISM, t_e, using

n_s

t_e = Q⁺_s (✏) Q_s (✏), (8)

Note that, in principle, te can come out negative, implying either some un-accounted for (perhaps primary) source for the species s, or a higher secondary production rate at an adjacent region in the Galaxy with positive net flow of s from that region into our local vicinity, or a deviation from steady-state. Finding a hint to any one of these

A local account of secondary cosmic rays

Kfir Blum^1,⇤ and Kohta Murase^1,†

1Institute for Advanced Study, Princeton 08540, USA

We calculate the total production rate per unit volume of high energy (10-150 GeV) secondary positron and antiproton cosmic rays in the local interstellar medium, over distances of order 500pc from the Solar System. Comparing the net production rate to the locally observed cosmic ray densities, we deduce a confinement time of cosmic rays in the solar neighborhood, of order t_e ⇡?.

This calculation serves as a sanity test for the secondary origin of high energy cosmic ray antimatter.

The result is...

Introduction.

n_B(R, ~r , t ) = Z

d³r Z

dt c ⇢_ISM(~r, t) 2

4 X

i=C,N,O,...

⇣ _i

!B

¯ m

⌘n_i(R, ~r, t) ⇣ _B

¯ m

⌘n_B(R, ~r, t) 3

5 P (R; {~r, t}, {~r , t })

= 2

4 X

i=C,N,O,...

⇣ i!B

¯ m

⌘ n_i(R, ~r , t ) ⇣

B

¯ m

⌘n_B(R, ~r , t ) 3 5 Z

d³r Z

dt c ⇢_ISM(~r, t) n_C (R, ~r, t)

n_C (R, ~r , t ) P (R; {~r, t}, {~r , t }) F^B

⇡ QB(R) Xesc(R) (1)

Q_B(R) = X

i=C,N,O,...

⇣ i!B

¯ m

⌘

n_i(R, ~r , t ) ⇣

B

¯ m

⌘

n_B(R, ~r , t ) (2)

Q_B(R, ~r, t) = X

i=C,N,O,...

⇣ _i

!B

¯ m

⌘n_i(R, ~r, t) ⇣ _B

¯ m

⌘n_B(R, ~r, t) (3)

X_esc = Z

d³r Z

dt c ⇢_ISM(~r, t) n_C (R, ~r, t)

n_C (R, ~r , t ) P (R; {~r, t}, {~r , t }) (4)

F_B =

P

i=C,N,O,... ^i!Bm¯

ni(R,~r,t)

n_C(R,~r,t) m¯^B

nB(R,~r,t) n_C(R,~r,t)

P

i=C,N,O,... ^i!Bm¯

n_i(R,~r ,t )

nC(R,~r ,t ) m¯^B

n_B(R,~r ,t ) nC(R,~r ,t )

⇡ 1 (5)

n_A(R)

n_B(R) = Q_A(R)

Q_B(R) (6)

n_A

n_B = Q_A

Q_B (7)

n_A(R) = QA(R) ⇥ Xesc(R) (8)

Gamma ray observations provide evidence that the spectrum and density of CRs in the interstellar medium (ISM) on moderate distances (100-500pc) from the Solar System are approximately uniform, and consistent with the local measurements outside of the Earth’s atmosphere. Combining the locally measured CR flux with estimates of the mass of ISM gas in the solar neighborhood, we can therefore calculate the production rate of secondary CRs in this region.

This calculation is free of modeling assumptions for the distribution and propagation of CRs, that apply on larger spatial scales.

Comparing the calculated local net production rate of secondary CRs to their observed densities, we can infer the trapping time of the CRs in the local ISM, t_e, using

n_s

t_e = Q⁺_s (✏) Q_s (✏), (9)

Engelmann et al (1990)

equivalent to:

•  Empirical relation:

•  = Local net production per unit column density of target, for species A

•  = “mean column density” ≈ 8.7(R/10GV)^-0.4 g/cm². No species label

Engelmann et al (1990)

Stable secondaries with no energy loss (boron, pbar, sub-Fe,…)

A local account of secondary cosmic rays

Kfir Blum^1,⇤ and Kohta Murase^1,†

1Institute for Advanced Study, Princeton 08540, USA

We calculate the total production rate per unit volume of high energy (10-150 GeV) secondary positron and antiproton cosmic rays in the local interstellar medium, over distances of order 500pc from the Solar System. Comparing the net production rate to the locally observed cosmic ray densities, we deduce a confinement time of cosmic rays in the solar neighborhood, of order t_e ⇡?.

This calculation serves as a sanity test for the secondary origin of high energy cosmic ray antimatter.

The result is...

Introduction.

n_B(R, ~r , t ) = Z

d³r Z

dt c ⇢_ISM(~r, t) 2

4 X

i=C,N,O,...

⇣ _i

!B

¯ m

⌘n_i(R, ~r, t) ⇣ _B

¯ m

⌘n_B(R, ~r, t) 3

5 P (R; {~r, t}, {~r , t })

= 2

4 X

i=C,N,O,...

⇣ i!B

¯ m

⌘

n_i(R, ~r , t ) ⇣

B

¯ m

⌘

n_B(R, ~r , t ) 3 5 Z

d³r Z

dt c ⇢_ISM(~r, t) n_C (R, ~r, t)

n_C (R, ~r , t ) P (R; {~r, t}, {~r , t }) F^B

⇡ Q^B(R) X^esc(R) (1)

Q_B(R) = X

i=C,N,O,...

⇣ i!B

¯ m

⌘

n_i(R, ~r , t ) ⇣

B

¯ m

⌘

n_B(R, ~r , t ) (2)

Q_B(R, ~r, t) = X

i=C,N,O,...

⇣ _i

!B

¯ m

⌘n_i(R, ~r, t) ⇣ _B

¯ m

⌘n_B(R, ~r, t) (3)

X_esc = Z

d³r Z

dt c ⇢_ISM(~r, t) n_C (R, ~r, t)

n_C (R, ~r , t ) P (R; {~r, t}, {~r , t }) (4)

F_B =

P

i=C,N,O,... ⁱm^!B¯

ni(R,~r,t)

nC(R,~r,t) m¯^B

nB(R,~r,t) nC(R,~r,t)

P

i=C,N,O,... ^i!Bm¯

ni(R,~r ,t )

n_C(R,~r ,t ) m¯^B

nB(R,~r ,t ) n_C(R,~r ,t )

⇡ 1 (5)

n_A(R)

n_B(R) = Q_A(R)

Q_B(R) (6)

n_A(R) = Q^A(R) ⇥ X^esc(R) (7)

Gamma ray observations provide evidence that the spectrum and density of CRs in the interstellar medium (ISM) on moderate distances (100-500pc) from the Solar System are approximately uniform, and consistent with the local measurements outside of the Earth’s atmosphere. Combining the locally measured CR flux with estimates of the mass of ISM gas in the solar neighborhood, we can therefore calculate the production rate of secondary CRs in this region.

This calculation is free of modeling assumptions for the distribution and propagation of CRs, that apply on larger spatial scales.

Comparing the calculated local net production rate of secondary CRs to their observed densities, we can infer the trapping time of the CRs in the local ISM, t_e, using

n_s

t_e = Q⁺_s (✏) Q_s (✏), (8)

Note that, in principle, t_e can come out negative, implying either some un-accounted for (perhaps primary) source for the species s, or a higher secondary production rate at an adjacent region in the Galaxy with positive net flow of s from that region into our local vicinity, or a deviation from steady-state. Finding a hint to any one of these

A local account of secondary cosmic rays

Kfir Blum

^{1, ⇤}

and Kohta Murase

^{1, †}

1Institute for Advanced Study, Princeton 08540, USA

We calculate the total production rate per unit volume of high energy (10-150 GeV) secondary positron and antiproton cosmic rays in the local interstellar medium, over distances of order 500pc from the Solar System. Comparing the net production rate to the locally observed cosmic ray densities, we deduce a confinement time of cosmic rays in the solar neighborhood, of order te ⇡?.

This calculation serves as a sanity test for the secondary origin of high energy cosmic ray antimatter.

The result is...

Introduction.

n

_B

( R, ~r , t ) = Z

d

³

r Z

dt c ⇢

_ISM

(~r, t) 2

4 X

i=C,N,O,...

⇣

_i

!B

¯ m

⌘ n

_i

( R, ~r, t) ⇣

_B

¯ m

⌘ n

_B

( R, ~r, t) 3

5 P (R; {~r, t}, {~r , t })

= 2

4 X

i=C,N,O,...

⇣

_i

!B

¯ m

⌘ n

_i

( R, ~r , t ) ⇣

_B

¯ m

⌘ n

_B

( R, ~r , t ) 3 5 Z

d

³

r Z

dt c ⇢

_ISM

(~r, t) n

_C

( R, ~r, t)

n

_C

( R, ~r , t ) P ( R; {~r, t}, {~r , t }) F

^B

⇡ Q

^B

( R) X

^esc

( R) (1)

Q

_B

( R) = X

i=C,N,O,...

⇣

_i

!B

¯ m

⌘ n

_i

( R, ~r , t ) ⇣

_B

¯ m

⌘ n

_B

( R, ~r , t ) (2)

Q

_B

( R, ~r, t) = X

i=C,N,O,...

⇣

_i

!B

¯ m

⌘ n

_i

( R, ~r, t) ⇣

_B

¯ m

⌘ n

_B

( R, ~r, t) (3)

X

_esc

= Z

d

³

r Z

dt c ⇢

_ISM

(~r, t) n

_C

( R, ~r, t)

n

_C

( R, ~r , t ) P ( R; {~r, t}, {~r , t }) (4)

F

_B

=

P

i=C,N,O,... ⁱm^!B¯

ni(R,~r,t)

nC(R,~r,t) m¯^B

nB(R,~r,t) nC(R,~r,t)

P

i=C,N,O,... ⁱm^!B¯

n_i(R,~r ,t )

n_C(R,~r ,t ) m¯^B

n_B(R,~r ,t ) n_C(R,~r ,t )

⇡ 1 (5)

n

_A

( R)

n

_B

( R) = Q

_A

( R)

Q

_B

( R) (6)

n

_A

( R) = Q

^A

( R) ⇥ X

^esc

( R) (7)

Gamma ray observations provide evidence that the spectrum and density of CRs in the interstellar medium (ISM) on moderate distances (100-500pc) from the Solar System are approximately uniform, and consistent with the local measurements outside of the Earth’s atmosphere. Combining the locally measured CR flux with estimates of the mass of ISM gas in the solar neighborhood, we can therefore calculate the production rate of secondary CRs in this region.

This calculation is free of modeling assumptions for the distribution and propagation of CRs, that apply on larger spatial scales.

Comparing the calculated local net production rate of secondary CRs to their observed densities, we can infer the trapping time of the CRs in the local ISM, t

_e

, using

n

_s

t

_e

= Q

⁺_s

(✏) Q

_s

(✏), (8)

Note that, in principle, t

_e

can come out negative, implying either some un-accounted for (perhaps primary) source for the species s, or a higher secondary production rate at an adjacent region in the Galaxy with positive net flow of s from that region into our local vicinity, or a deviation from steady-state. Finding a hint to any one of these A local account of secondary cosmic rays

Kfir Blum^1,⇤ and Kohta Murase^{1, †}

1Institute for Advanced Study, Princeton 08540, USA

We calculate the total production rate per unit volume of high energy (10-150 GeV) secondary positron and antiproton cosmic rays in the local interstellar medium, over distances of order 500pc from the Solar System. Comparing the net production rate to the locally observed cosmic ray densities, we deduce a confinement time of cosmic rays in the solar neighborhood, of order te ⇡?.

This calculation serves as a sanity test for the secondary origin of high energy cosmic ray antimatter.

The result is...

Introduction.

n_B(R, ~r , t ) = Z

d³r Z

dt c ⇢_ISM(~r, t) 2

4 X

i=C,N,O,...

⇣ _i

!B

¯ m

⌘n_i(R, ~r, t) ⇣ _B

¯ m

⌘n_B(R, ~r, t) 3

5 P (R; {~r, t}, {~r , t })

= 2

4 X

i=C,N,O,...

⇣ _i

!B

¯ m

⌘n_i(R, ~r , t ) ⇣ _B

¯ m

⌘n_B(R, ~r , t ) 3 5 Z

d³r Z

dt c ⇢_ISM(~r, t) n_C (R, ~r, t)

n_C (R, ~r , t ) P (R; {~r, t}, {~r , t }) F^B

⇡ Q^B(R) X^esc(R) (1)

Q_B(R) = X

i=C,N,O,...

⇣ _i

!B

¯ m

⌘n_i(R, ~r , t ) ⇣ _B

¯ m

⌘n_B(R, ~r , t ) (2)

Q_B(R, ~r, t) = X

i=C,N,O,...

⇣ _i

!B

¯ m

⌘n_i(R, ~r, t) ⇣ _B

¯ m

⌘n_B(R, ~r, t) (3)

X_esc = Z

d³r Z

dt c ⇢_ISM(~r, t) nC (R, ~r, t)

n_C (R, ~r , t ) P (R; {~r, t}, {~r , t }) (4)

FB =

P

i=C,N,O,... ⁱm^!B¯

ni(R,~r,t)

nC(R,~r,t) m¯^B

nB(R,~r,t) nC(R,~r,t)

P

i=C,N,O,... ⁱm^!B¯

ni(R,~r ,t )

nC(R,~r ,t ) m¯^B

nB(R,~r ,t ) nC(R,~r ,t )

⇡ 1 (5)

n_A(R)

n_B(R) = Q_A(R)

Q_B(R) (6)

n_A(R) = Q^A(R) ⇥ X^esc(R) (7)

Gamma ray observations provide evidence that the spectrum and density of CRs in the interstellar medium (ISM) on moderate distances (100-500pc) from the Solar System are approximately uniform, and consistent with the local measurements outside of the Earth’s atmosphere. Combining the locally measured CR flux with estimates of the mass of ISM gas in the solar neighborhood, we can therefore calculate the production rate of secondary CRs in this region.

This calculation is free of modeling assumptions for the distribution and propagation of CRs, that apply on larger spatial scales.

Comparing the calculated local net production rate of secondary CRs to their observed densities, we can infer the trapping time of the CRs in the local ISM, t_e, using

n_s

t_e = Q⁺_s (✏) Q_s (✏), (8)

Note that, in principle, te can come out negative, implying either some un-accounted for (perhaps primary) source for the species s, or a higher secondary production rate at an adjacent region in the Galaxy with positive net flow of s from that region into our local vicinity, or a deviation from steady-state. Finding a hint to any one of these

A local account of secondary cosmic rays

Kfir Blum^1,⇤ and Kohta Murase^1,†

1Institute for Advanced Study, Princeton 08540, USA

We calculate the total production rate per unit volume of high energy (10-150 GeV) secondary positron and antiproton cosmic rays in the local interstellar medium, over distances of order 500pc from the Solar System. Comparing the net production rate to the locally observed cosmic ray densities, we deduce a confinement time of cosmic rays in the solar neighborhood, of order t_e ⇡?.

This calculation serves as a sanity test for the secondary origin of high energy cosmic ray antimatter.

The result is...

Introduction.

n_B(R, ~r , t ) = Z

d³r Z

dt c ⇢_ISM(~r, t) 2

4 X

i=C,N,O,...

⇣ _i

!B

¯ m

⌘n_i(R, ~r, t) ⇣ _B

¯ m

⌘n_B(R, ~r, t) 3

5 P (R; {~r, t}, {~r , t })

= 2

4 X

i=C,N,O,...

⇣ i!B

¯ m

⌘ n_i(R, ~r , t ) ⇣

B

¯ m

⌘n_B(R, ~r , t ) 3 5 Z

d³r Z

dt c ⇢_ISM(~r, t) n_C (R, ~r, t)

n_C (R, ~r , t ) P (R; {~r, t}, {~r , t }) F^B

⇡ QB(R) Xesc(R) (1)

Q_B(R) = X

i=C,N,O,...

⇣ i!B

¯ m

⌘

n_i(R, ~r , t ) ⇣

B

¯ m

⌘

n_B(R, ~r , t ) (2)

Q_B(R, ~r, t) = X

i=C,N,O,...

⇣ _i

!B

¯ m

⌘n_i(R, ~r, t) ⇣ _B

¯ m

⌘n_B(R, ~r, t) (3)

X_esc = Z

d³r Z

dt c ⇢_ISM(~r, t) n_C (R, ~r, t)

n_C (R, ~r , t ) P (R; {~r, t}, {~r , t }) (4)

F_B =

P

i=C,N,O,... ^i!Bm¯

ni(R,~r,t)

n_C(R,~r,t) m¯^B

nB(R,~r,t) n_C(R,~r,t)

P

i=C,N,O,... ^i!Bm¯

n_i(R,~r ,t )

nC(R,~r ,t ) m¯^B

n_B(R,~r ,t ) nC(R,~r ,t )

⇡ 1 (5)

n_A(R)

n_B(R) = Q_A(R)

Q_B(R) (6)

n_A

n_B = Q_A

Q_B (7)

n_A(R) = QA(R) ⇥ Xesc(R) (8)

Gamma ray observations provide evidence that the spectrum and density of CRs in the interstellar medium (ISM) on moderate distances (100-500pc) from the Solar System are approximately uniform, and consistent with the local measurements outside of the Earth’s atmosphere. Combining the locally measured CR flux with estimates of the mass of ISM gas in the solar neighborhood, we can therefore calculate the production rate of secondary CRs in this region.

This calculation is free of modeling assumptions for the distribution and propagation of CRs, that apply on larger spatial scales.

Comparing the calculated local net production rate of secondary CRs to their observed densities, we can infer the trapping time of the CRs in the local ISM, t_e, using

n_s

t_e = Q⁺_s (✏) Q_s (✏), (9)

Stable secondaries with no energy loss

Theoretically, this is a natural relation.

Guaranteed to apply if the composition of CRs and ISM is uniform (well mixed) in the region of the Galaxy where spallation happens*

*Check out first 2 extra slides

NGC 891

1.4GHz NIR

A local account of secondary cosmic rays

Kfir Blum

^{1, ⇤}

and Kohta Murase

^{1, †}

1Institute for Advanced Study, Princeton 08540, USA

We calculate the total production rate per unit volume of high energy (10-150 GeV) secondary positron and antiproton cosmic rays in the local interstellar medium, over distances of order 500pc from the Solar System. Comparing the net production rate to the locally observed cosmic ray densities, we deduce a confinement time of cosmic rays in the solar neighborhood, of order te ⇡?.

This calculation serves as a sanity test for the secondary origin of high energy cosmic ray antimatter.

The result is...

Introduction.

n

_B

( R, ~r , t ) = Z

d

³

r Z

dt c ⇢

_ISM

(~r, t) 2

4 X

i=C,N,O,...

⇣

_i!B

¯ m

⌘ n

_i

( R, ~r, t) ⇣

_B

¯ m

⌘ n

_B

( R, ~r, t) 3

5 P (R; {~r, t}, {~r , t })

= 2

4 X

i=C,N,O,...

⇣

_i

!B

¯ m

⌘ n

_i

( R, ~r , t ) ⇣

_B

¯ m

⌘ n

_B

( R, ~r , t ) 3 5 Z

d

³

r Z

dt c ⇢

_ISM

(~r, t) n

_C

( R, ~r, t)

n

_C

( R, ~r , t ) P ( R; {~r, t}, {~r , t }) F

^B

⇡ Q

^B

( R) X

^esc

( R) (1)

Q

_B

( R) = X

i=C,N,O,...

⇣

_i

!B

¯ m

⌘ n

_i

( R, ~r , t ) ⇣

_B

¯ m

⌘ n

_B

( R, ~r , t ) (2)

Q

_B

( R, ~r, t) = X

i=C,N,O,...

⇣

_i

!B

¯ m

⌘ n

_i

( R, ~r, t) ⇣

_B

¯ m

⌘ n

_B

( R, ~r, t) (3)

X

_esc

= Z

d

³

r Z

dt c ⇢

_ISM

(~r, t) n

_C

( R, ~r, t)

n

_C

( R, ~r , t ) P ( R; {~r, t}, {~r , t }) (4)

F

_B

=

P

i=C,N,O,... ⁱm^!B¯

ni(R,~r,t)

nC(R,~r,t) m¯^B

n_B(R,~r,t) nC(R,~r,t)

P

i=C,N,O,... ⁱm^!B¯

ni(R,~r ,t )

n_C(R,~r ,t ) m¯^B

nB(R,~r ,t ) n_C(R,~r ,t )

⇡ 1 (5)

n

_A

( R)

n

_B

( R) = Q

_A

( R)

Q

_B

( R) (6)

n

_A

n

_B

= Q

_A

Q

_B

(7)

n

_A

( R) = Q

^A

( R) ⇥ X

^esc

( R) (8)

Gamma ray observations provide evidence that the spectrum and density of CRs in the interstellar medium (ISM) on moderate distances (100-500pc) from the Solar System are approximately uniform, and consistent with the local measurements outside of the Earth’s atmosphere. Combining the locally measured CR flux with estimates of the mass of ISM gas in the solar neighborhood, we can therefore calculate the production rate of secondary CRs in this region.

This calculation is free of modeling assumptions for the distribution and propagation of CRs, that apply on larger spatial scales.

Comparing the calculated local net production rate of secondary CRs to their observed densities, we can infer the trapping time of the CRs in the local ISM, t

_e

, using

n

_s

t

_e

= Q

⁺_s

(✏) Q

_s

(✏), (9)

Stable secondaries with no energy loss

Theoretically, this is a natural relation.

Do not need to assume homogeneous diffusion, boundary conditions, steady state,...

…and verifying this relation does not teach us that any

of these assumptions is correct

A local account of secondary cosmic rays

Kfir Blum

^{1, ⇤}

and Kohta Murase

^{1, †}

1Institute for Advanced Study, Princeton 08540, USA

We calculate the total production rate per unit volume of high energy (10-150 GeV) secondary positron and antiproton cosmic rays in the local interstellar medium, over distances of order 500pc from the Solar System. Comparing the net production rate to the locally observed cosmic ray densities, we deduce a confinement time of cosmic rays in the solar neighborhood, of order te ⇡?.

This calculation serves as a sanity test for the secondary origin of high energy cosmic ray antimatter.

The result is...

Introduction.

n

_B

( R, ~r , t ) = Z

d

³

r Z

dt c ⇢

_ISM

(~r, t) 2

4 X

i=C,N,O,...

⇣

_i!B

¯ m

⌘ n

_i

( R, ~r, t) ⇣

_B

¯ m

⌘ n

_B

( R, ~r, t) 3

5 P (R; {~r, t}, {~r , t })

= 2

4 X

i=C,N,O,...

⇣

_i

!B

¯ m

⌘ n

_i

( R, ~r , t ) ⇣

_B

¯ m

⌘ n

_B

( R, ~r , t ) 3 5 Z

d

³

r Z

dt c ⇢

_ISM

(~r, t) n

_C

( R, ~r, t)

n

_C

( R, ~r , t ) P ( R; {~r, t}, {~r , t }) F

^B

⇡ Q

^B

( R) X

^esc

( R) (1)

Q

_B

( R) = X

i=C,N,O,...

⇣

_i

!B

¯ m

⌘ n

_i

( R, ~r , t ) ⇣

_B

¯ m

⌘ n

_B

( R, ~r , t ) (2)

Q

_B

( R, ~r, t) = X

i=C,N,O,...

⇣

_i

!B

¯ m

⌘ n

_i

( R, ~r, t) ⇣

_B

¯ m

⌘ n

_B

( R, ~r, t) (3)

X

_esc

= Z

d

³

r Z

dt c ⇢

_ISM

(~r, t) n

_C

( R, ~r, t)

n

_C

( R, ~r , t ) P ( R; {~r, t}, {~r , t }) (4)

F

_B

=

P

i=C,N,O,... ⁱm^!B¯

ni(R,~r,t)

nC(R,~r,t) m¯^B

n_B(R,~r,t) nC(R,~r,t)

P

i=C,N,O,... ⁱm^!B¯

ni(R,~r ,t )

n_C(R,~r ,t ) m¯^B

nB(R,~r ,t ) n_C(R,~r ,t )

⇡ 1 (5)

n

_A

( R)

n

_B

( R) = Q

_A

( R)

Q

_B

( R) (6)

n

_A

n

_B

= Q

_A

Q

_B

(7)

n

_A

( R) = Q

^A

( R) ⇥ X

^esc

( R) (8)

Gamma ray observations provide evidence that the spectrum and density of CRs in the interstellar medium (ISM) on moderate distances (100-500pc) from the Solar System are approximately uniform, and consistent with the local measurements outside of the Earth’s atmosphere. Combining the locally measured CR flux with estimates of the mass of ISM gas in the solar neighborhood, we can therefore calculate the production rate of secondary CRs in this region.

This calculation is free of modeling assumptions for the distribution and propagation of CRs, that apply on larger spatial scales.

Comparing the calculated local net production rate of secondary CRs to their observed densities, we can infer the trapping time of the CRs in the local ISM, t

_e

, using

n

_s

t

_e

= Q

⁺_s

(✏) Q

_s

(✏), (9)

diffusion models fit the grammage

Maurin, Donato, Taillet, Salati Astrophys.J.555:585-596,2001

2L

K~(E/Z)^δ

diffusion models fit the grammage

2L

K~(E/Z)^δ

antiprotons

antiprotons Tan & Ng 1982,1983

A local account of secondary cosmic rays

Kfir Blum^{1, ⇤} and Kohta Murase^1,†

1Institute for Advanced Study, Princeton 08540, USA

We calculate the total production rate per unit volume of high energy (10-150 GeV) secondary positron and antiproton cosmic rays in the local interstellar medium, over distances of order 500pc from the Solar System. Comparing the net production rate to the locally observed cosmic ray densities, we deduce a confinement time of cosmic rays in the solar neighborhood, of order te ⇡?.

This calculation serves as a sanity test for the secondary origin of high energy cosmic ray antimatter.

The result is...

Introduction.

n_B(R, ~r , t ) = Z

d³r Z

dt c ⇢_ISM(~r, t) 2

4 X

i=C,N,O,...

⇣ i!B

¯ m

⌘n_i(R, ~r, t) ⇣

B

¯ m

⌘ n_B(R, ~r, t) 3

5 P (R; {~r, t}, {~r , t })

= 2

4 X

i=C,N,O,...

⇣ _i

!B

¯ m

⌘n_i(R, ~r , t ) ⇣ _B

¯ m

⌘n_B(R, ~r , t ) 3 5 Z

d³r Z

dt c ⇢_ISM(~r, t) n_C (R, ~r, t)

n_C (R, ~r , t ) P (R; {~r, t}, {~r , t }) F^B

⇡ Q^B(R) X^esc(R) (1)

Q_B(R) = X

i=C,N,O,...

⇣ i!B

¯ m

⌘n_i(R, ~r , t ) ⇣

B

¯ m

⌘n_B(R, ~r , t ) (2)

Q_B(R, ~r, t) = X

i=C,N,O,...

⇣ _i

!B

¯ m

⌘n_i(R, ~r, t) ⇣ _B

¯ m

⌘ n_B(R, ~r, t) (3)

X_esc = Z

d³r Z

dt c ⇢_ISM(~r, t) n_C (R, ~r, t)

n_C (R, ~r , t ) P (R; {~r, t}, {~r , t }) (4)

F_B =

P

i=C,N,O,... ⁱm^!B¯

ni(R,~r,t)

nC(R,~r,t) m¯^B

nB(R,~r,t) nC(R,~r,t)

P

i=C,N,O,... ⁱm^!B¯

ni(R,~r ,t )

nC(R,~r ,t ) m¯^B

nB(R,~r ,t ) nC(R,~r ,t )

⇡ 1 (5)

n_A(R)

n_B(R) = Q_A(R)

Q_B(R) (6)

n_A

n_B = Q_A

Q_B (7)

n_A(R) = Q^A(R) ⇥ X^esc(R) (8)

J_p¯

J_p = 10^{1 p} ⇣_p,A>1¯ C_p,pp¯ ^pp,inel m_p

X_esc 1 + _m^p¯

p X_esc (9)

Gamma ray observations provide evidence that the spectrum and density of CRs in the interstellar medium (ISM) on moderate distances (100-500pc) from the Solar System are approximately uniform, and consistent with the local measurements outside of the Earth’s atmosphere. Combining the locally measured CR flux with estimates of the mass of ISM gas in the solar neighborhood, we can therefore calculate the production rate of secondary CRs in this region.

This calculation is free of modeling assumptions for the distribution and propagation of CRs, that apply on larger spatial scales.

antiprotons

antiprotons

AMS02 Antiprotons look

very secondary to me.

1.  There should not be a cut-off at higher energy 2.  Should be

viewed together w/ B/C

positrons

A local account of secondary cosmic rays

Kfir Blum

^{1, ⇤}

and Kohta Murase

^{1, †}

1

Institute for Advanced Study, Princeton 08540, USA

We calculate the total production rate per unit volume of high energy (10-150 GeV) secondary positron and antiproton cosmic rays in the local interstellar medium, over distances of order 500pc from the Solar System. Comparing the net production rate to the locally observed cosmic ray densities, we deduce a confinement time of cosmic rays in the solar neighborhood, of order t

e

⇡?.

This calculation serves as a sanity test for the secondary origin of high energy cosmic ray antimatter.

The result is...

Introduction.

n

_B

( R, ~r , t ) = Z

d

³

r Z

dt c ⇢

_ISM

(~r, t) 2

4 X

i=C,N,O,...

⇣

_i

!B

¯ m

⌘ n

_i

( R, ~r, t) ⇣

_B

¯ m

⌘ n

_B

( R, ~r, t) 3

5 P (R; {~r, t}, {~r , t })

= 2

4 X

i=C,N,O,...

⇣

_i

!B

¯ m

⌘ n

_i

( R, ~r , t ) ⇣

_B

¯ m

⌘ n

_B

( R, ~r , t ) 3 5 Z

d

³

r Z

dt c ⇢

_ISM

(~r, t) n

_C

( R, ~r, t)

n

_C

( R, ~r , t ) P ( R; {~r, t}, {~r , t }) F

^B

⇡ Q

^B

( R) X

^esc

( R) (1)

Q

_B

( R) = X

i=C,N,O,...

⇣

_i

!B

¯ m

⌘ n

_i

( R, ~r , t ) ⇣

_B

¯ m

⌘ n

_B

( R, ~r , t ) (2)

Q

_B

( R, ~r, t) = X

i=C,N,O,...

⇣

_i

!B

¯ m

⌘ n

_i

( R, ~r, t) ⇣

_B

¯ m

⌘ n

_B

( R, ~r, t) (3)

X

_esc

= Z

d

³

r Z

dt c ⇢

_ISM

(~r, t) n

_C

( R, ~r, t)

n

_C

( R, ~r , t ) P ( R; {~r, t}, {~r , t }) (4)

F

_B

=

P

i=C,N,O,... ⁱm^!B¯

n_i(R,~r,t)

n_C(R,~r,t) m¯^B

n_B(R,~r,t) n_C(R,~r,t)

P

i=C,N,O,... ⁱm^!B¯

n_i(R,~r ,t )

n_C(R,~r ,t ) m¯^B

n_B(R,~r ,t ) n_C(R,~r ,t )

⇡ 1 (5)

n

_A

( R)

n

_B

( R) = Q

_A

( R)

Q

_B

( R) (6)

n

_A

n

_B

= Q

_A

Q

_B

(7)

n

_A

( R) = Q

^A

( R) ⇥ X

^esc

( R) (8)

J

_p¯

J

_p

= 10

^{1 p}

⇣

_p,A>1¯

C

_p,pp¯ ^pp,inel

m

_p

X

_esc

1 +

_m^p¯

p

X

_esc

(9)

J

_e⁺

J

_p

= f

_e⁺

⇥ 10

^{1 p}

⇣

_e⁺_,A>1

C

_e⁺_,pp ^pp,inel

m

_p

X

_esc

(10)

Gamma ray observations provide evidence that the spectrum and density of CRs in the interstellar medium (ISM)

on moderate distances (100-500pc) from the Solar System are approximately uniform, and consistent with the local