limit on the axion decay constant from the cooling …seminar/pdf_2019_zenki/...limit on the axion...

Limit on the Axion Decay Constant from the Cooling Neutron Star in Cassiopeia A

Natsumi Nagata

K. Hamaguchi, N. Nagata, K. Yanagi, and J. Zheng, Phys. Rev. D98, 103015 (2018).

Seminar @ Osaka UniversityApr. 16, 2019

University of Tokyo

Outline

Cassiopeia A (Cas A) Neutron Star

Standard Neutron Star Cooling and Cas A

Axion Emission from Neutron Star

Limit on Axion Decay Constant

Conclusion

Cas A NS

1980JHA....11....1A

3 Cassiopeiae

3 Cassiopeiae

Atlas Coelestis (1729)

John FlamsteedFirst Astronomer Royal

He recorded 3 Cassiopeiae on August 16, 1680.

Never been observed since then.

Cassiopeia A (Cas A)

Supernova remnant

Chandra (2011).

Explosion date estimated from the remnant expansion: 1681 ± 19.Neutron star (NS) was found in the center.

d = 3.4+0.3−0.1 kpc

Cas A NS Cooling

Cooling of Cas A NSdirectly observed.

Chandra

The Astrophysical Journal Letters, 719:L167–L171, 2010 August 20 doi:10.1088/2041-8205/719/2/L167C⃝ 2010. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

DIRECT OBSERVATION OF THE COOLING OF THE CASSIOPEIA A NEUTRON STAR

Craig O. Heinke1 and Wynn C. G. Ho21 Department of Physics, University of Alberta, Room 238 CEB, Edmonton, AB T6G 2G7, Canada; [email protected]

2 School of Mathematics, University of Southampton, Southampton SO17 1BJ, UK; [email protected] 2010 April 14; accepted 2010 July 8; published 2010 August 2

ABSTRACT

The cooling rate of young neutron stars (NSs) gives direct insight into their internal makeup. Although thetemperatures of several young NSs have been measured, until now a young NS has never been observed to decreasein temperature over time. We fit nine years of archival Chandra ACIS spectra of the likely NS in the ∼330 yr oldCassiopeia A supernova remnant with our non-magnetic carbon atmosphere model. Our fits show a relative declinein the surface temperature by 4% (5.4σ , from (2.12±0.01)×106 K in 2000 to (2.04±0.01)×106 K in 2009) and theobserved flux by 21%. Using a simple model for NS cooling, we show that this temperature decline could indicatethat the NS became isothermal sometime between 1965 and 1980, and constrains some combinations of neutrinoemission mechanisms and envelope compositions. However, the NS is likely to have become isothermal soon afterformation, in which case the temperature history suggests episodes of additional heating or more rapid cooling.Observations over the next few years will allow us to test possible explanations for the temperature evolution.

Key words: dense matter – neutrinos – pulsars: general – stars: neutron – supernovae: individual (Cassiopeia A) –X-rays: stars

Online-only material: color figures

1. INTRODUCTION

The internal composition and structure of neutron stars (NSs)remain unclear (e.g., Lattimer & Prakash 2004). Areas ofuncertainty include whether exotic condensates occur in theNS core, the symmetry energy and thus proton fraction in thecore, the behavior of superfluidity among neutrons and protons,the conductivity of the NS crust, and the chemical compositionof the outer envelope. NSs are heated to billions of degreesduring supernovae and cooled via a combination of neutrinoand photon emission. Observing the cooling rates of youngNSs is a critical method to constrain the uncertainties (seeTsuruta 1998; Yakovlev & Pethick 2004; Page et al. 2006 forreviews).

To date, observations of young cooling NSs have beenrestricted to measuring the temperature of individual NSsat one point in time. As NSs may differ in their masses,envelope compositions, etc., a measurement of the cooling rateof a young NS is needed to determine its cooling trajectory.Since neutrino radiation (rather than the observed photonradiation) is the dominant source of cooling during the first∼105 years, measurements of cooling rates during this timerequire measuring a temperature decline over time. No youngNS has previously been observed to cool steadily over time.Though the ∼106 year old NS RX J0720.4−3125 has showntemperature variations of ∼10% over ≈ 7 years (de Vries et al.2004; Hohle et al. 2009), this variation is ascribed to either aglitch-like event or precession of surface hot spots (Haberl et al.2006; van Kerkwijk et al. 2007; Hohle et al. 2009). Magnetars,such as 4U 0142+61, have shown temperature variations, alongwith changes in their pulsed fraction and pulse profile (Dib et al.2007), but these are likely due to magnetic field reconfigurationevents.

The compact central object at the center of the Cassiopeia A(Cas A) supernova remnant was discovered in Chandra’s first-light observations (Tananbaum 1999) and quickly identifiedas a likely NS, which we assume here. It is presently theyoungest-known NS, as the remnant’s estimated age is ≈ 330 yr

(Fesen et al. 2006). It is relatively close-by (d = 3.4+0.3−0.1 kpc;

Reed et al. 1995) and the supernova remnant has been wellstudied, with over a megasecond of Chandra ACIS observationsspread over 10 years (Hwang et al. 2004; DeLaney et al.2004; Patnaude & Fesen 2007, 2009). However, its spectrum(modeled as a blackbody or a magnetic or non-magnetichydrogen atmosphere) was inconsistent with emission from thefull surface of the NS (Pavlov et al. 2000; Chakrabarty et al.2001; Pavlov & Luna 2009). Timing investigations using theChandra High Resolution Camera (HRC) and XMM-Newtonhave failed to identify pulsations down to a pulsed fractionlevel of <12% (Murray et al. 2002; Mereghetti et al. 2002;Ransom 2002; Halpern & Gotthelf 2010), indicating that theemission is probably from the entire surface. These apparentlycontradictory observations are reconciled by the discovery thatan unmagnetized (B < 1011 G) carbon atmosphere provides agood fit to the Chandra ACIS data, with the emission arisingfrom the entire surface of the Cas A NS (Ho & Heinke 2009).

Pavlov et al. (2004) examined two long ACIS observations(50 ks each) of the Cas A NS from 2000 and 2002, alongwith several short (2.5 ks) calibration observations, finding nosignificant changes in flux. Upon re-examination of archivalEinstein and ROSAT data, the NS was only barely detectedand thus could not be used to search for variability (Pavlovet al. 2000). Pavlov & Luna (2009) mention that the fluxmeasured in their 2006 observation is slightly lower than thatreported previously, but do not attempt to determine whetherthe difference is real. Before Ho & Heinke (2009), it was notexpected that the emission arises from the entire surface of theNS, so further serious searches for temperature variations werenot undertaken. Here, we utilize the full Chandra ACIS archiveof Cas A NS observations to measure the temperature changesfrom 2000 to 2009.

2. X-RAY ANALYSIS

We analyzed all Chandra ACIS-S exposures without grat-ings, longer than 5 ks of Cas A, listed in Table 1. We also

L167

• This was rather rapid.

• This is the only NS whose cooling curve is observed for the moment.

Today’s topic

D. Pager, M. Prakash, J. M. Lattimer, and A. W. Steiner, Phys .Rev. Lett. 106, 081101 (2011);P. S. Shternin, D. G. Yakovlev, C. O. Heinke, W. C. G. Ho, and D. J. Patnaude, MNRS 412, L108 (2011).

Observed cooling curve of the Cas A NS can be explained by the standard cooling theory.

This might be spoiled if there is an extra cooling source such as axion.

Neutron superfluidity plays an important role.

We may give a limit on such a cooling source.

Standard NS Cooling and Cas A

Size of neutron star vs Osaka

Neutrons, protons, electrons are degenerate.Neutrons and protons are in superfluidity and superconductivity.

Radius ~10 km1—2 M⦿

As high as nuclear density.

Neutron star structure

~ 1 km

Outer crustNeutron-rich nucleus (crystal)

Inner crust

Neutron-rich nucleus, electron

Neutron superfluid:

Outer core

Electron, muonNeutron superfluid:Proton superconductor:

Inner coreNeutron superfluid:Hyperons, π/K condensation, quarks (?)

Electron

1S0

3P2

3P2

1S0

We do not consider them in this talk.

Envelope, atmosphere

Standard Cooling of NSD. Pager, J. M. Lattimer, M. Prakash, A. W. Steiner, Astrophys. J. Suppl. 155, 623 (2004);

M. E. Gusakov, A. D. Kaminker, D. G. Yakovlev, O. Y. Gnedin, Astron. Astrophys. 423, 1063 (2004).

Consider a NS composed of

NeutronsProtonsLeptons (e, μ)

Nucleon superfluidity taken into account.

Equation for temperature evolution

C(T)dTdt

= − Lν − Lγ

C(T): Stellar heat capacityLν: Luminosity of neutrino emissionLγ: Luminosity of photon emission

Thermal relaxation completed at t ≲ 100 yrs

Cooling sourcesTwo cooling sources:

ν

γPhoton emission (from surface)

Dominant for t ≳ 105 years

Neutrino emission (from core)

Direct Urca process (DUrca)

Modified Urca process (MUrca)

Bremsstrahlung

PBF processt ≲ 105 yearsDominant for

PBF process occurs only in thepresence of nucleon superfluidity.

cf.) Cas A NS: ~ 338 yrs

Neutrino emission

e!_

!_

e!_

n

np

n

p

e e !

n

Modified Urca BremsstrahlungDirect Urca

n n n n

nn

These processes occur only near the Fermi surface.

pF ≫ T, mn − mp

These processes can occur in a non-superfluid NS core.

f(p)

1

0pF

p

T

Name: UrcaA P I& I L 1, 1941 PIC YSI CAL REVIEW VOLUME 59

Neutrino Theory of Stellar CollapseG. GAMow, George Washington University, Washington, D. C.M. ScHQENBERG, University of Sao Paulo, Sao Paulo, Brazil

(Received February 6, 1941)

At the very high temperatures and densities which mustexist in the interior of contracting stars during the laterstages of their evolution, one must expect a special typeof nuclear processes accompanied by the emission of a largenumber of neutrinos. These neutrinos penetrating almostwithout difficulty the body of the star, must carry awayvery large amounts of energy and prevent the centraltemperature from rising above a certain limit. This mustcause a rapid contraction of the stellar body ultimatelyresulting in a catastrophic collapse. It is shown that energylosses through the neutrinos produced in reactions between

free electrons and oxygen nuclei can cause a completecollapse of the star within the time period of half an hour.Although the main energy losses in such collapses are dueto neutrino emission which escapes direct observation.the heating of the body of a collapsing star must necessarilylead to the rapid expansion of the outer layers and thetremendous increase of luminosity. It is suggested thatstellar collapses of this kind are responsible for the phe-nomena of novae and supernovae, the difference betweenthe two being probably due to the diR'erence of theirmasses.

)1. INTRQDUcTIQN

1

~ONEof the most peculia. r phenomena which

we encounter in the evolutionary life ofstars consists in vast stellar explosions known as"ordinary novae" and "supernovae. " It is nowwell established that, although these two classesof novae possess a great many features in com-nlon, they are sharply separated insofar as theirmaximum luminosities are concerned. The ordi-nary novae, appearing at the rate of about 50 peryear in our stellar system, reach at their maxi-mum a luminosity of the order of magnitude of10' suns. On the other hand, the supernovae,Haring up in any given stellar system only once inseveral centuries, reach luminosities exceedingthat of the sun by a factor of 10'. The inter-mediate luminosities have never been observed, .

and there seems to exist a real gap between thesetwo classes of stellar explosions.

The common features of novae and supernovaemay be briefly summarized as follows:

(1) Both ordinary novae and supernovae showa very similar form of luminosity curve (apartfrom the luminosity scale, of course) with a sharprise to the maximum within a few days or weeks,and a subsequent slow decline of intensity,decreasing by a factor of two every four or fivemonths.

(2) In both cases the spectrum shows ratherhigh surface temperature (up to 20,000'C for

* Now at George Washington University as Fellow ofthe Guggenheim Foundation.

ordinary novae, and probably above 30,000'Cfor supernovae), and the rapid expansion of thestellar atn1osphere which is evidently blown upby the increasing radiative pressure. In the caseof Nova Aquilae 1918, for example, the star wassurrounded by a luminous gas shell expandingwith a velocity of 2000 kilometers per second,whereas the gas masses expelled by the galacticsupernova of the year A.D. 1054 (observed byChinese astronomers) form at present an ex-tensive luminous cloud known as the "Crab-Nebula. " It must be noticed here that the largesurface area of this blown-up atmosphere ismainly responsible for the observed high lumi-nosities, since the increase of the surface tempera-ture can only account for a factor of severalhundreds in the surface brightness.

(3) Whereas the "prenovae, " in the rare caseswhen they have been observed, represent com-paratively normal stars of the spectral class A(surface temperature about 10,000'C), ' the"postnovae, "remaining after the Hare-up, possessextremely high surface temperatures (spectralclass 0) and seem to represent highly collapsedconfigurations, such as the stars of the "Wolf-Rayet" type.

The same evidently holds true for the case of

The meagerness of observational material makes itimpossible to decide whether "prenovae" are located onthe main sequence or to the left of it. There seems to beno doubt, however, that, as the result of explosion, theposition of the star in the Hertzsprung-Russell diagram isstrongly shifted towards higher surface temperatures andsmaller radii.

539

540 (". . G A M 0 W A N D M. SCHOENBERG

supernovae, since the star found in the center ofthe "Crab-Nebula, "and representing most proba-bly the remainder of the galactic supernova A.D.1054, shows the typical features of a very dense"white dwarf. "The change of state caused by these stellar

catastrophes strongly suggests that the processinvolved here is not connected with any instan-taneous liberation of intranuclear energy due tosome explosive reaction, but rather represents arapid collapse of the entire stellar body as wasfirst suggested by Milne. 'It was suggested by Baade and Zwicky, ' in

particular application to supernovae, that suchcollapses may be due to the formation within thestar of a large number of neutrons which wouldpermit considerably closer "packing" in thecentral regions.It is easy to see, however, that the possibility

of closer packing alone is quite insufficient toexplain the rapid collapse of the star, since such acollapse requires the removal of large amounts ofgravitational energy produced by contraction in

the interior of the star. In fact, quite independentof whether the matter in the center consists ofcharged nuclei or neutrons, the heat produced bycontraction must pass through the entire body ofthe star, and the rate of energy transport, de-pending on the opacity of the main body, will bethe same in both cases. On the other hand, if wecan find some way of removing instantaneouslythe heat liberated in the central regions, in spiteOf the opacity of the stellar body, the star will

collapse with a velocity comparable to that of"free fall" independent of the kind of particlesexisting in its interior.The amount of gravitational energy which is

liberated when a star of a mass M contracts fromthe original radius Rp to the collapsed radius R, isgiven approximately by

companion of Sirius (R.=Ro/40), ' the total liber-ation of gravitational energy will be of the orderof magnitude of 10"erg. On the other hand, thetime of the free-fall collapse from the originalradius Ro to any small value of the radius is givenapproximately by

In the case of the sun, At will be of the order10'sec. (i.e. , about half an hour), so that the meanrate of energy removal necessary for such acollapse is about 10" erg/g sec. If we rememberthat the collapse of novae and supernovae takesplace within a few days, we come to the con-clusion that the rate of energy removal in theseactual cases may be only several hundred timessmaller than given above.As we suggested in a recent publication, ' this

very fast removal of energy from the interior ofthe star can be understood on the basis of thepresent ideas on the role of neutrinos in nucleartransformations involving emission or absorptionof P-particles. In fact, when the temperature anddensity in the interior of a contracting star reachcertain values depending on the kind of nucleiinvolved, we should expect processes of the type

zN~+e —+z ~X'+antineutrino

g ~X —+zN +e +neutrino,

which we shall call, for brevity, "urea-processes. "The neutrinos formed in the above processes'absorb a considerable part of the transformationenergy (about ~3), and escape with practically nodifhculty through the body of the star.As we shall see later, these processes of ab-

sorption and reemission of free electrons bycertain atomic nuclei which are abundant instellar matter may lead to such tremendousenergy losses through the neutrino emission that

Thus, for example, if a star of the mass andradius of our sun contracts to the size of the

~ E. A. Milne, Observatory 54, 145 (1931).3 W. Baade and F. Zwicky, Proc. Nat. Acad. Sci. 20,

259 (1934).

4 The companion of Sirius possesses a mass which isalmost equal to the mass of the sun, and may be consideredas representing the type of the white dwarfs obtained bythe collapse of the sun.G. Gamow and M. Schoenberg, Phys. Rev. 58, 1117

(1940).'We shall use the term "neutrino" both for ordinary

neutrinos and antineutrinos involved in the reaction,since there is no noticeable difference in their behavior.It is also clear that one can neglect the possibility of mutualanniJ'ilation of these particles witkin a stellar body, sincethey escape from the star with practically no collisions.

Named after a casino inRio de Janeiro:

Cassino da Urca

To commemorate the casino where they first met.

Rapid disappearance of energy (money) of a star (gambler).

UnRecordable Cooling Agent.

“Urca” means “thief” in Russian.

Direct Urca process

(Neutrino momentum, ~ T, is negligible.)

To satisfy the momentum conservation in the DUrca process

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is required.

Emissivity (energy loss rate per unit time & volume)

QD ' 4⇥ 1027 ⇥✓

T

109 K

◆6

⇥(pF,p + pF,e � pF,n) erg · cm�3 · s�1

<latexit sha1_base64="0VVlHbTUoJSh4SqEM+aYPddgQXg=">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</latexit><latexit sha1_base64="0VVlHbTUoJSh4SqEM+aYPddgQXg=">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</latexit><latexit sha1_base64="0VVlHbTUoJSh4SqEM+aYPddgQXg=">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</latexit><latexit sha1_base64="K+GKYvez7jEllRm45rU4TJAD3Nw=">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</latexit>

This dominates other processes (if occurs).e!

_!_

e!_

n

np

n

p

e e !

n


n n n n

nn

Direct Urca condition

0

100

200

300

400

500

600

0 2 4 6 8 10

DU

rca

allo

wed

M = 2.0M�, R = 10.93 km

p F[M

eV]

Radial distance [km]

pF,npF,p + pF,e

0

100

200

300

400

500

0 2 4 6 8 10

M = 1.4M�, R = 11.43 km

p F[M

eV]

Radial distance [km]

pF,npF,p + pF,e

This process can occur only at high-density regions.

Only massive stars ( ) allow this process.W/ APR equation of state.

≳ 2M⊙

Direct Urca in Cas A NSThe mass of Cas A NS is estimated to be

M ≃ (1.4 ± 0.3)M⊙

K. G. Elshamouty, C. O. Heinke, W. C. Ho, A. Y. Potekhin, Phys .Rev. C91, 015806 (2015).

Direct Urca does not operate in Cas A NS.

Slow neutrino emission processes

e!_

!_

e!_

n

np

n

p

e e !

n


n n n n

nn

∝ T8

Nucleon pairingNucleons in a NS form pairings below their critical temperatures:

Neutron singlet 1S0

Proton singlet 1S0

Proton triplet 3P2

Only in the crust. Less important.

} Form in the core. Important.

BCS

Co

reC

rust

GMB

GC

SCLBL2.5

2.0

1.5

1.0

0.5

0

k [fm ]

1.5

F−1

T

[10

K]

c1

0

∆[M

eV]

2.0

1.5

1.0

0.5

00 0.5 1.0

SFB

WAPCCDK

GIPSF

Neutron singlet pairing gap

T

[1

0

K]

9c

BS

F−1

1.0 1.4 1.8 2.0

Cru

st−

Core

1.50 0.5 1.00

2

4

6

8

10

AO

T

CCY BCLL

EEHO

CCDK

2BF+3BF

k [fm ]

BS 2BF

[MeV

]

1.5

0.5

1.0

∆

0

Proton singlet pairing gap

D. Page, J. M. Lattimer, M. Prakash, A. W. Steiner [arXiv: 1302.6626].

Effects of nucleon paringsIn the presence of pairing gap, the energy of quasi-particle is

This gap introduces a suppression factor to

∝ e− ΔNT

Slow neutrino emission process

Heat capacity

In addition, a new neutrino emission process is turned on:

Pair-breaking and formation (PBF) process

PBF process

PB

F

10 P

32

ν_

ν

n n

1.0

T/T

Co

ntr

ol

fun

cti

on

R

S

0.5

c

0.0 0.2 0.4 0.6 0.8 1.00.0

∆

Thermal disturbance induces the breaking of nucleon pairs.

During the reformation of cooper pairs, the gap energy is released via neutrino emission.

This process significantly enhances the neutrino emission only when

T ≲ TC

If T > TC, this process does not occur.If T << TC, pair breaking rarely occurs.

Summary for standard cooling

Photon emission

Direct Urca process

Unimportant in Cas A NS.

Does not operate in Cas A NS.

Modified Urca & bremsstrahlung

Suppressed after the onset of nucleon superfluidity.

PBFStrongly enhances the neutrino emission at T ≲ TC

Surface temperatureIt is the surface temperature that we observe, so we need torelate it to the internal temperature.

g14: surface gravity in units of 1014 cm s-2.ΔM: mass of light elements.

As the amount of light elements gets increased, the surface temperature becomes larger. Light elements have large thermal conductivities.

A. Y. Potekhin, G. Chabrier, and D. G. Yakovlev, A&A 323, 415 (1997).

This relation depends on the amount of light elements in the envelope.

η ≡ g214ΔM/M

Success of Standard Cooling

M = (1.01 − 1.92)M⊙

O. Y. Gnedin, M. Gusakov, A. Kaminker, D. G. Yakovlev, Mon. Not. Roy. Astron. Soc. 363, 555 (2005).

Standard cooling scenario can explain most of the data.

Cas A NS cooling2

havior and test whether this theoretical behavior matchesthe observed behavior. To do this fully consistently, acomplete NS model requires a self-consistent calculationof the EOS and superfluid and superconducting gap en-ergies. However, this has not been done up to the presenttime. Therefore we assume that the EOS and gap modelsare decoupled, as in [13, 14]. We also assume standard(i.e., minimal) cooling [13, 15], since cooling by fast neu-trino emission processes, such as direct Urca, producestemperatures that are far too low at the current age ofthe Cas A NS (∼ 330 yr; [16]). With these assumptions,we perform for the first time consistent fitting of both theCas A NS spectra and temperature evolution for the NSmass and radius. We find that the mass and radius canbe determined very accurately for a given EOS and gapenergies. However there are sufficient observational andtheoretical uncertainties that we cannot claim to rule outspecific EOS and gap energy models. One of the mainpurposes of this work is to motivate nuclear physiciststo not only calculate the EOS, but also superfluid andsuperconducting gap energies, and to provide them in auseful way to the astrophysicists.In Sec. II, we discuss our new observations of the Cas A

NS. In Sec. III, we briefly describe our NS model, includ-ing the EOS and superfluid and superconducting gaps. InSec. IV, we present our results. Finally, we summarizeand discuss our conclusions in Sec. V.

II. CAS A TEMPERATURE DATA, INCLUDINGNEW CHANDRA OBSERVATIONS

The two new data points are from 49-ks and 50-ksACIS-S Graded observations taken on 2013 May 20 (Ob-sID 14480) and 2014 May 12 (ObsID 14481), respectively.We use the Chandra Interactive Analysis of Observations(CIAO) 4.5 software and Chandra Calibration Database(CALDB) 4.5.5.1 to analyze all the ACIS-S Graded ob-servations. For each observation, we calculate ancillaryresponse functions, including corrections for the fractionof the point-spread function enclosed in an extraction re-gion. We fit all the spectra simultaneously to measure NSsurface temperatures using the non-magnetic partiallyionized carbon atmosphere models of [5], adopting thesame fitting parameters as in [4, 11], and holding the NSmass and radius, distance, and hydrogen column densityfixed between observations. Further details are describedin [4] (see also [17]). The results are shown in Table I.Note that in the present work, we consider the rapid cool-ing rate derived from only these ACIS-S Graded data;future work will consider the lower cooling rates foundby [4, 17].Since the Cas A NS belongs to a class of NSs known

as central compact objects (CCOs) and three membersof this class have surface magnetic fields ∼ 1010− 1011 G(the interior field may be much higher; see [18, 19]), wealso attempt to fit the relatively low magnetic field hydro-gen atmosphere model spectra described in [19]; note that

TABLE I. Chandra ACIS-S Graded mode temperatures.

ObsID Year Teffa

114 2000.08 2.145+0.009−0.008

1952 2002.10 2.142+0.009−0.008

5196 2004.11 2.118+0.011−0.007

(9117,9773)b 2007.93 2.095+0.007−0.010

(10935,12020)b 2009.84 2.080+0.009−0.008

(10936,13177)b 2010.83 2.070+0.009−0.009

14229 2012.37 2.050+0.009−0.008

14480 2013.38 2.075+0.009−0.009

14481 2014.36 2.045+0.009−0.009

a Errors are 1σ.b The two ObsIDs, which were taken close together in time withthe same instrument setup, are merged prior to spectralanalysis.

the model spectra currently available at field strengths(1, 4, 7, 10)×1010 G are computed for only surface gravity= 2.4 × 1014 cm s−2. At the high temperatures presentat early NS ages, nuclear burning rapidly removes surfacehydrogen and helium [20, 21]. However, non-hydrogen at-mosphere models for the relevant magnetic fields do notcurrently exist. Also, even though the hydrogen modelspectra we use are for a fully ionized atmosphere, the fit-ted temperatures are high (Teff > 106 K), such that spec-tral features due to any trace amounts of bound speciesdo not significantly affect the spectra [22]. The resultingfits can be good (with χ2

ν ≈ 1 for 337 degrees of free-dom) but have unrealistically small NS mass and radius(< 0.4MSun and ∼ 5 km), and thus we do not considerthese models further.

III. NEUTRON STAR MODEL

A. Equation of state

To construct non-rotating equilibrium NSs, we solvethe Tolman-Oppenheimer-Volkoff relativistic equationsof stellar structure (see, e.g., [23]), supplemented by theEOS. We consider three nuclear EOSs: The first is APR,specifically A18+δv+UIX∗ [24], with the neutron andproton effective masses given by the analytic formula in[13], and is the same EOS that is used in [12–14]. Theother two are BSk20 and BSk21 [25], which are calculatedusing the analytic functions in [26], with the nucleon ef-fective masses given by the analytic formula in [27] andparameters in [28]. BSk20 and BSk21 use generalizedSkyrme forces and are constructed to satisfy various ex-perimental constraints (see [26] and references therein)and to be similar to APR of [24] and V18 of [29], respec-tively. In addition, the crust composition predicted byBSk21 is compatible with the recent nuclear mass mea-surement of [30]. All three EOSs produce a NS withmaximum mass > 2MSun, as needed to match the (high-

Cas A NS temperature data

Can we explain this cooling behavior with the standard cooling scenario??

3—4% decreasein ten years.


[×106 K]

How to explain Cas A cooling

Only 0.3% decrease in T in ten years.

Observation

3—4% decrease in ten years.

Modified Urca/Bremsstrahlung

Rapid cooling but does not last so long.

PBF

If PBF process has just started recently, the Cas A NS cooling can be explained.

Fit in the minimal cooling paradigm

CT = 10 KT = 0CCT = 5.5x10 K8

9

D. Pager, M. Prakash, J. M. Lattimer, and A. W. Steiner, Phys .Rev. Lett. 106, 081101 (2011).

If the critical temperature of neutrino triplet pairing is

T(n)C ∼ 5 × 108 K PBF has just started.

Cas A NS cooling can be explained.

Direct evidence of superfluidity in NS

Rapid Cooling of the Neutron Star in Cassiopeia ATriggeredby Neutron Superfluidity in Dense Matter

Dany Page,1 Madappa Prakash,2 James M. Lattimer,3 and Andrew W. Steiner4

1Instituto de Astronomıa, Universidad Nacional Autonoma de Mexico, Mexico D.F. 04510, Mexico2Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701-2979, USA

3Department of Physics and Astronomy, State University of New York at Stony Brook, Stony Brook, New York 11794-3800, USA4Joint Institute for Nuclear Astrophysics, National Superconducting Cyclotron Laboratory and, Department of Physics

and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA(Received 29 November 2010; published 22 February 2011)

We propose that the observed cooling of the neutron star in Cassiopeia A is due to enhanced neutrino

emission from the recent onset of the breaking and formation of neutron Cooper pairs in the 3P2 channel.

We find that the critical temperature for this superfluid transition is ’ 0:5! 109 K. The observed rapidity

of the cooling implies that protons were already in a superconducting state with a larger critical

temperature. This is the first direct evidence that superfluidity and superconductivity occur at supranuclear

densities within neutron stars. Our prediction that this cooling will continue for several decades at the

present rate can be tested by continuous monitoring of this neutron star.

DOI: 10.1103/PhysRevLett.106.081101 PACS numbers: 97.60.Jd, 95.30.Cq, 26.60."c

The neutron star in Cassiopeia A (Cas A), discovered in1999 in the Chandra first light observation [1] targeting thesupernova remnant, is the youngest known in the MilkyWay. An association with the historical supernova SN 1680[2] gives Cas A an age of 330 yr, in agreement with itskinematic age [3]. The distance to the remnant is estimatedto be 3:4þ0:3

"0:1 kpc [4]. The thermal soft x-ray spectrum ofCas A is well fit by a nonmagnetized carbon atmospheremodel, with a surface temperature of 2! 106 K andan emitting radius of 8–17 km [5]. These results raiseCas A to the rank of the very few isolated neutron starswith a well determined age and a reliable surface tempera-ture, thus allowing for detailed modeling of its thermalevolution and the determination of its interior proper-ties [6].

Analyzing archival data from 2000–2009, Heinke andHo [7] recently reported that Cas A’s surface temperaturehas rapidly decreased from 2:12! 106 to 2:04! 106 K[8,9]. This rate of cooling is significantly larger than ex-pected from the modified Urca (‘‘MU’’) process [10,11] ora medium modified Urca [12]. It is also unlikely to be dueto any of the fast neutrino (!) emission processes (such asdirect Urca processes from nucleons or hyperons, or !emission from Bose condensates or gapless quark matter)since the visible effects of those become apparent overthe thermal relaxation time scale of the crust [13]; i.e.,30–100 yr, much earlier than the age of Cas A, and exhibita slow evolution at later times. We interpret Cas A’scooling within the ‘‘minimal cooling’’ paradigm [14] andsuggest it is due to the recent triggering of enhancedneutrino emission resulting from the neutron 3P2 pairingin the star’s core. Our numerical calculations and analyticalanalysis imply a critical temperature TC ’ 0:5! 109 K forthe triplet neutron superfluidity.

The essence of the minimal cooling paradigm is thea priori exclusion of all fast !-emission mechanisms,thus restricting ! emission to the ‘‘standard’’ MU processand nucleon bremsstrahlung processes [11]. However, ef-fects of pairing, i.e., neutron superfluidity and/or protonsuperconductivity, are included. At temperatures just be-low the critical temperature Tc of a pairing phase transi-tion, the continuous breaking and formation of Cooperpairs [15], referred to as the ‘‘PBF’’ process, results inan enhanced neutrino emission. Calculations of Tc forneutrons, Tcn, in the 3P2 channel relevant for neutron starcores, are uncertain due to unsettled interactions [16] andmedium effects which can either strongly suppress orincrease the pairing [17]. Consequently, predictions rangefrom vanishingly small to almost 1011 K [14]. The pairinggap is density (") dependent, and the resulting Tcnð"Þcommonly exhibits a bell-shaped density profile.Assuming the neutron star has an isothermal core at tem-perature T, the phase transition will start when T reaches,at some location in the star, the maximum value of Tcnð"Þ:TC & maxTcnð"Þ. At that stage, neutrons in a thick shell gothrough the phase transition and as T decreases, this shellsplits into two shells which slowly drift toward the lowerand higher density regions away from the maximum of thebell-shaped profile. If the neutron 3P2 gap has the appro-priate size, ! emission from the PBF process is an order ofmagnitude more efficient than the MU process (see Fig. 20of [14] or Fig. 2 of [18]).Implications of the size of the neutron 3P2 pairing

gap were considered in [19] with the result that, forTC < 109 K, a neutron star would go through the pairingphase transition at ages ranging from hundreds to tensof thousands of years, accompanied by a short phase ofrapid cooling. This phenomenon, illustrated in Fig. 6 of

PRL 106, 081101 (2011)

Selected for a Viewpoint in PhysicsPHY S I CA L R EV I EW LE T T E R S

week ending25 FEBRUARY 2011

0031-9007=11=106(8)=081101(4) 081101-1 ! 2011 American Physical Society

Rapid Cooling of the Neutron Star in Cassiopeia ATriggeredby Neutron Superfluidity in Dense Matter

Dany Page,1 Madappa Prakash,2 James M. Lattimer,3 and Andrew W. Steiner4

1Instituto de Astronomıa, Universidad Nacional Autonoma de Mexico, Mexico D.F. 04510, Mexico2Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701-2979, USA

3Department of Physics and Astronomy, State University of New York at Stony Brook, Stony Brook, New York 11794-3800, USA4Joint Institute for Nuclear Astrophysics, National Superconducting Cyclotron Laboratory and, Department of Physics

and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA(Received 29 November 2010; published 22 February 2011)

We propose that the observed cooling of the neutron star in Cassiopeia A is due to enhanced neutrino

emission from the recent onset of the breaking and formation of neutron Cooper pairs in the 3P2 channel.

We find that the critical temperature for this superfluid transition is ’ 0:5! 109 K. The observed rapidity

of the cooling implies that protons were already in a superconducting state with a larger critical

temperature. This is the first direct evidence that superfluidity and superconductivity occur at supranuclear

densities within neutron stars. Our prediction that this cooling will continue for several decades at the

present rate can be tested by continuous monitoring of this neutron star.

DOI: 10.1103/PhysRevLett.106.081101 PACS numbers: 97.60.Jd, 95.30.Cq, 26.60."c

The neutron star in Cassiopeia A (Cas A), discovered in1999 in the Chandra first light observation [1] targeting thesupernova remnant, is the youngest known in the MilkyWay. An association with the historical supernova SN 1680[2] gives Cas A an age of 330 yr, in agreement with itskinematic age [3]. The distance to the remnant is estimatedto be 3:4þ0:3

"0:1 kpc [4]. The thermal soft x-ray spectrum ofCas A is well fit by a nonmagnetized carbon atmospheremodel, with a surface temperature of 2! 106 K andan emitting radius of 8–17 km [5]. These results raiseCas A to the rank of the very few isolated neutron starswith a well determined age and a reliable surface tempera-ture, thus allowing for detailed modeling of its thermalevolution and the determination of its interior proper-ties [6].

Analyzing archival data from 2000–2009, Heinke andHo [7] recently reported that Cas A’s surface temperaturehas rapidly decreased from 2:12! 106 to 2:04! 106 K[8,9]. This rate of cooling is significantly larger than ex-pected from the modified Urca (‘‘MU’’) process [10,11] ora medium modified Urca [12]. It is also unlikely to be dueto any of the fast neutrino (!) emission processes (such asdirect Urca processes from nucleons or hyperons, or !emission from Bose condensates or gapless quark matter)since the visible effects of those become apparent overthe thermal relaxation time scale of the crust [13]; i.e.,30–100 yr, much earlier than the age of Cas A, and exhibita slow evolution at later times. We interpret Cas A’scooling within the ‘‘minimal cooling’’ paradigm [14] andsuggest it is due to the recent triggering of enhancedneutrino emission resulting from the neutron 3P2 pairingin the star’s core. Our numerical calculations and analyticalanalysis imply a critical temperature TC ’ 0:5! 109 K forthe triplet neutron superfluidity.

The essence of the minimal cooling paradigm is thea priori exclusion of all fast !-emission mechanisms,thus restricting ! emission to the ‘‘standard’’ MU processand nucleon bremsstrahlung processes [11]. However, ef-fects of pairing, i.e., neutron superfluidity and/or protonsuperconductivity, are included. At temperatures just be-low the critical temperature Tc of a pairing phase transi-tion, the continuous breaking and formation of Cooperpairs [15], referred to as the ‘‘PBF’’ process, results inan enhanced neutrino emission. Calculations of Tc forneutrons, Tcn, in the 3P2 channel relevant for neutron starcores, are uncertain due to unsettled interactions [16] andmedium effects which can either strongly suppress orincrease the pairing [17]. Consequently, predictions rangefrom vanishingly small to almost 1011 K [14]. The pairinggap is density (") dependent, and the resulting Tcnð"Þcommonly exhibits a bell-shaped density profile.Assuming the neutron star has an isothermal core at tem-perature T, the phase transition will start when T reaches,at some location in the star, the maximum value of Tcnð"Þ:TC & maxTcnð"Þ. At that stage, neutrons in a thick shell gothrough the phase transition and as T decreases, this shellsplits into two shells which slowly drift toward the lowerand higher density regions away from the maximum of thebell-shaped profile. If the neutron 3P2 gap has the appro-priate size, ! emission from the PBF process is an order ofmagnitude more efficient than the MU process (see Fig. 20of [14] or Fig. 2 of [18]).Implications of the size of the neutron 3P2 pairing

gap were considered in [19] with the result that, forTC < 109 K, a neutron star would go through the pairingphase transition at ages ranging from hundreds to tensof thousands of years, accompanied by a short phase ofrapid cooling. This phenomenon, illustrated in Fig. 6 of

PRL 106, 081101 (2011)

Selected for a Viewpoint in PhysicsPHY S I CA L R EV I EW LE T T E R S

week ending25 FEBRUARY 2011

0031-9007=11=106(8)=081101(4) 081101-1 ! 2011 American Physical Society

Mon. Not. R. Astron. Soc. 412, L108–L112 (2011) doi:10.1111/j.1745-3933.2011.01015.x

Cooling neutron star in the Cassiopeia A supernova remnant: evidencefor superfluidity in the core

Peter S. Shternin,1,2⋆ Dmitry G. Yakovlev,1 Craig O. Heinke,3 Wynn C. G. Ho4⋆

and Daniel J. Patnaude5

1Ioffe Physical Technical Institute, Politekhnicheskaya 26, 194021 St Petersburg, Russia2St Petersburg State Polytechnical University, Politechnicheskaya 29, 195251 St Petersburg, Russia3Department of Physics, University of Alberta, Room 238 CEB, 11322-89 Avenue, Edmonton, AB T6G 2G7, Canada4School of Mathematics, University of Southampton, Southampton SO17 1BJ5Smithsonian Astrophysical Observatory, Cambridge, MA 02138, USA

Accepted 2011 January 12. Received 2011 January 12; in original form 2010 November 30

ABSTRACTAccording to recent results of Ho & Heinke, the Cassiopeia A supernova remnant con-tains a young (≈330-yr-old) neutron star (NS) which has carbon atmosphere and showsnotable decline of the effective surface temperature. We report a new (2010 November)Chandra observation which confirms the previously reported decline rate. The decline isnaturally explained if neutrons have recently become superfluid (in triplet state) in theNS core, producing a splash of neutrino emission due to Cooper pair formation (CPF) processthat currently accelerates the cooling. This scenario puts stringent constraints on poorly knownproperties of NS cores: on density dependence of the temperature Tcn(ρ) for the onset of neu-tron superfluidity [Tcn(ρ) should have a wide peak with maximum ≈ (7–9) × 108 K]; on thereduction factor q of CPF process by collective effects in superfluid matter (q > 0.4) and on theintensity of neutrino emission before the onset of neutron superfluidity (30–100 times weakerthan the standard modified Urca process). This is serious evidence for nucleon superfluidityin NS cores that comes from observations of cooling NSs.

Key words: dense matter – equation of state – neutrinos – stars: neutron – supernovae:individual: Cassiopeia A – X-rays: stars.

1 I N T RO D U C T I O N

It is well known that neutron star (NS) cores contain superdense mat-ter whose properties are still uncertain (see e.g. Haensel, Potekhin& Yakovlev 2007; Lattimer & Prakash 2007). One can explore theseproperties by studying the cooling of isolated NSs (see e.g. Pethick1992; Yakovlev & Pethick 2004; Page, Geppert & Weber 2006;Page et al. 2009 for review).

We analyse observations of the NS in the supernova remnant Cas-siopeia A (Cas A). The distance to the remnant is d = 3.4+0.3

−0.1 kpc(Reed et al. 1995). The Cas A age is reliably estimated as t ≈330 ± 20 yr from observations of the remnant expansion (Fesenet al. 2006). The compact central source was identified in first lightChandra X-ray observations (Tananbaum 1999) and studied byPavlov et al. (2000), Chakrabarty et al. (2001), and Pavlov & Luna(2009), but its nature has been uncertain. The fits of the observedX-ray spectrum with magnetized or non-magnetized hydrogen at-

⋆E-mail: [email protected] (PSS); [email protected](WCGH)

mosphere models or with blackbody spectrum revealed too smallsize of the emission region (could be hotspots on NS surface al-though no pulsations have been observed, e.g. Pavlov & Luna 2009).

Recently Ho & Heinke (2009) have shown that the observed spec-trum is successfully fitted taking a carbon atmosphere model witha low magnetic field (B ! 1011 G). The gravitational mass of theobject, as inferred from the fits, is M ≈ 1.3–2 M⊙, circumferentialradius R ≈ 8–15 km and the non-redshifted effective surface tem-perature T s ∼ 2 × 106 K (Yakovlev et al. 2011). These parametersindicate that the compact source is an NS with the carbon atmo-sphere. It emits thermal radiation from the entire surface and hasthe surface temperature typical for an isolated NS. It is the youngestin the family of observed cooling NSs.

Yakovlev et al. (2011) compared these observations with the NScooling theory. The authors concluded that the Cas A NS has alreadyreached the stage of internal thermal relaxation. It cools via neutrinoemission from the stellar core; its neutrino luminosity is not verydifferent from that provided by the modified Urca process.

Following Ho & Heinke (2009), Heinke & Ho (2010) analysedChandra observations of the Cas A NS during 10 yr and founda steady decline of Ts by about 4 per cent. They interpret it as

C⃝ 2011 The AuthorsMonthly Notices of the Royal Astronomical Society C⃝ 2011 RASDownloaded from https://academic.oup.com/mnrasl/article-abstract/412/1/L108/1007778

by University of Tokyo Library useron 04 June 2018







































Cooling source and Cas A NS

Data

Minimal Cooling

We consider axion as a cooling source.

If there is a cooling source,

W/ Cooling source

TemperatureCooling rate

decrease.

Limit on the cooling source!

Cas A NS data cannot be explained.

Axion emission from NS

Axion-nucleon couplings

KSVZ axion model

Cq = 0 Cp = − 0.47(3), Cn = − 0.02(3)

Note that Cn may be zero within uncertainty.

DFSZ axion model

J. E. Kim (1970); M. A. Shifman, A. I. Vainshtein, V. I. Zakharov (1980).

A. R. Zhitnitsky (1980); M. Dine, W. Fischler, M. Srednicki (1981).

Cu,c,t =13

cos2 β, Cd,s,b =13

sin2 β

Cp = − 0.182(25) − 0.435 sin2 β

Cn = − 0.160(25) + 0.414 sin2 β Both can be sizable.

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C(T )dTdt

= − Lν − Lγ − Lcool

Axion emission processesEquation for temperature evolution

Axion emission processes

PBFBremsstrahlung

We have modified NSCool to implement these processes.

Technical details

M = 1.4M⊙

Not so relevant.

Any gap models are fine as long as it is large enough.

Regard gap height (∝ TC) and width as free parameters.(Highly uncertain)

APR equation of state

NS mass:

Neutron 1S0 gap: SFB model

Proton 1S0 gap: CCDK model

Neutron 3P2 gap

Luminosity of axion emission

Onset of neutron triplet pairing.

Neutron PBF

Axion emission can be as strong as neutrino emission.

Axion emission is sizable even if Cn ≃ 0


Luminosity of axion emission

Axion emission is stronger than the KSVZ case.


Limit on axion decay constant

Core temperature of Cas A NSInferred core temperature @ Cas A NS age (Jan. 30, 2000)

η = 5 × 10−13

Band: t = 300—338 yearsNo neutron triplet superfluidity

Core temperature is too low for fa ≲ a few × 108 GeVLarge uncertainty due to the ignorance of the envelope properties.


Cooling curves vs data

We obtained a bound comparable to other astrophysical limits.

Our limit

fa ≳ 5 (7) × 108 GeVKSVZ (DFSZ, tanβ = 10)

Cf.) SN1987A

fa ≳ 4 × 108 GeV (KSVZ)


PDG 2019

Recent update

Four new datawere announced.

M. J. P. Wijingaarden, et. al., MNRAS 484, 974 (2019).

Cas A NS temperature is still decreasing!! ~ 2% in ten yrs.

Additional data, observations of different NSs, etc., allow us totest the NS cooling theory.

We are working on more detailed analysis with this new data.

K. Hamaguchi, N. Nagata, K. Yanagi, and J. Zheng, in preparation.

Conclusion

Conclusion

• Observed rapid cooling of Cas A NS can be explained in the minimal cooling scenario.

• Presence of additional cooling source may spoil the success, which thus restricts such possibilities.

• We obtain a lower limit on the axion decay constant, which is as strong as existing astrophysical bounds.

Backup

Temperature distributionBA C D

13

1030

100

300

"Pit

"

Core

Cru

st

Neu

tron d

rip

Oute

r boundar

y

1000

Slow cooling

Fast coolingq=27

Paired

("PBF" turned off)

Paired

Normal

q=26q=25

Normal


Relaxation in the Coredone in ~ 100 years.

Relaxation in the presence of axion

Direct Urca process

Neutrino chemical potential is zero.

So, as long as the above approximation is valid, the typicalsize of the Fermi momenta of protons and electrons are O(10) MeV.

Therefore, the Direct Urca process can occur only where the density is huge so that the above approximation is not valid.

Neutrino momentum is negligible.

Chemical equilibrium

Charge neutrality

Momentum conservation

Cooling curves

104

105

106

107

100 102 104 106

T[K

]

t [yrs]

1.4M�2.0M�

The direct Urca process affects the neutron star cooling significantly.

Spectral fit of Cas A NS

Non-magnetic carbon atmosphere model fits the X-ray spectrum of Cas A NS quite well.


C. O. Heinke, W. C. Ho, Nature 462, 71 (2009).

Through the gravitational redshift, we can infer the NS mass.

M ≃ (1.4 ± 0.3)M⊙

1S0 neutron gapBy solving the gap equation, we can obtain the pairing gap.

BCS

Core

Cru

st

GMB

GC

SCLBL2.5

2.0

1.5

1.0

0.5

0

k [fm ]

1.5

F−1

T [1

0 K

]c

10

∆[M

eV]

2.0

1.5

1.0

0.5

00 0.5 1.0

SFB

WAPCCDK

GIPSF

• BCS, GMB: a weak-limit approximated analytical solution without and with medium effects.

• Others: calculations using different models for nuclear potential.


1S0 proton gap


We use the CCDK model to suppress neutron emissionbefore the onset of neutron triplet pairing.

3P2 neutron gap1.4 2.01.8 1.0 1.4 2.01.8

SF

3bf

HGRR

NijI

CDB

AV182bf

AO T

Cru

st

Core NijII

a

b

c

a2

Cru

st

Core

1.0


Large theoretical uncertainty

Core and boundary temperature

Slow neutrino emissionTemperature evolution

C(T )dTdt

= − Lν

Heat capacity

C(T ) = C9T9, C9 ∼ 1039 erg ⋅ K−1

T9 = T/(109 K)

Lν = L9T89 , L9 ∼ 1040 erg ⋅ s−1

T9 = (C9 ⋅ 109 K6L9 t )

16

∼ (1 yeart )

16

Internal temperature goes as T ∝ t− 16

Modified Urca + Bremsstrahlung

T9 ≃ 0.1288 × (T4s6

g14 )0.455

E. H. Gudmundsson, C. J. Pethick, and R. I. Epstein (1983).

Ts6 = Ts/(106 K)

Surface vs internal temperatures

Slow neutrino emission and Cas A NSFrom the above formulae, we finally obtain Ts ∝ t−0.09

Only 0.3% decrease in T in ten years.

The slow neutrino emission cannot explain the observedrapid cooling of the Cas A NS.

Solution in the minimal cooling paradigm

Use the PBF process to enhance the cooling rate.

This process does not last so long.

We need to take the critical temperature to be just abovethe internal temperature of Cas A NS (~ 5 × 108 K).

Fit with minimal cooling


AxionAxion is a Nambu-Goldstone boson associated withthe Peccei-Quinn symmetry. R. D Peccei and H. R. Quinn (1977);

S. Weinberg (1978); F. Wilczek (1978).Lagrangian

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Axion-nucleon couplings

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Spin fractions

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Gluon contribution can be takeninto account as quark contributionsthrough a field rotation.

Large η in KSVZ


For large η, the core temperature gets small.

Cannot explain the rapid cooling of Cas A.

Other possibilitiesOther possibilities to explain the rapid cooling in Cas A NS are

Direct UrcaR. Nigreiros, S. Schramm, F. Weber, Phys. Lett. 718, 1176 (2013).

G. Taranto, G. F. Burgio, and H. J. Schulze, MNRAS 456, 1451 (2016).

[rotationally induced]

A. Bonanno, M. Baldo, G. F. Burgio, V. Urpin, A&A 561, L5 (2014). [+ heating by magnetic field decay]

Slow thermal relaxationD. Blaschke, H. Grigorian, D. N. Voskresensky, and F. Weber, Phys. Rev. 85, 022802 (2012).

D. Blaschke, H. Grigorian, D. N. Voskresensky, Phys. Rev. 88, 065805 (2013).

Stellar fluid oscillationsS. H. Yang, C. M. Pi, X. P. Zheng, APJ. 735, L29 (2011).

Quark color superconductingT. Noda, et. al., APJ. 765, 1 (2013).

Pairing in Nuclei

150 170 190 210 230 250

0.1

0.5

1.0

E (MeV)

Mass number A

odd−even/even−odd nuclei

even−even nuclei

G A

P

Lowest excitation levels of nuclei

A. Bohr, B. R. Mottelson, and D. Pines, Phys. Rev. 110, 936 (1958).

A nucleon in even-even nuclei requires a minimum energy for excitation.

Suggests the presence of a gap.

Pairing in NucleiBinding energy per nucleon

50 100 150 200 250Mass number A

8.6

8.0

7.4

E/A(MeV)

0

even−even nucleiodd−even/even−odd nuclei

E. Segre, Nuclei and Particles.

Even-even nuclei are more bound than odd-even/odd-odd nuclei.

Pairing in NucleiPhase shifts for nucleon-nucleon scattering

Spin−triplet pairs

S = 1

Spin−singlet pairs

L > 0

L = 0

S = 0

L > 0

L = 0

−20o

−30o

E (MeV)labN−N

E (MeV)F

(10 g cm )ρ 14 −3

Phase shift (in degrees)

o

20o

10o

0o

−10o

100 200 300 400 500 600

25 50

1 2

75

4

100

6 8

125

10 12

150

30

2

P3

1

S01

P32

D

41G

03P

01S

1

R. Tamagaki, Prog. Theor. Phys. 44, 905 (1970).

A positive phase-shift impliesan attractive interaction.

From this result, we expect

Nucleons pair in a spin-singlet state at low densities.

A spin-triplet pairing occurs at high densities.

Medium effects may modify the interactions.

Pairing effects on neutron star cooling

32

S10

P32

S10P3

2

Contr

ol

funct

ion R

ν

T/Tc T/Tc

1.0

0.5

0.0

1

2

3

p n

2.432.19

0.2 0.4 0.6 0.8 1.00

0.2 0.4 0.6 0.8 1.0

Specific Heat

Contr

ol

funct

ion R

Neutrino Emission

C

S10 P


Due to the energy gap, available phase space is limited at low temperatures.

Cooling by neutrino emission is suppressed.Specific heat is suppressed.Cooper pair breaking and formation enhance neutrino emission

limit on the axion decay constant from the cooling …seminar/pdf_2019_zenki/...limit on the axion...

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