The observability of isolated neutron stars and black holes.

Fa oltà di S ienze Matemati he, Fisi he e Naturali

Dottorato di Ri er a in Astronomia e Astrosi a

Tesidi Dottorato

THE OBSERVABILITY OF ISOLATED

NEUTRON STARS AND BLACK HOLES

Supervisor:

Prof. Aldo Treves

Ni ola Sartore

Matri ola 708043

XXIII

o

Ci lo

PREFACE 5

1 INTRODUCTION 7

1.1 Neutronstars . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2 Bla k holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3 The past 40years . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 MONTE CARLO SIMULATIONS OF NEUTRON STAR ORBITS 19 2.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.1.1 Distributionof progenitors . . . . . . . . . . . . . . . . 20

2.1.2 Birthvelo ities . . . . . . . . . . . . . . . . . . . . . . 26

2.1.3 Gravitationalpotential . . . . . . . . . . . . . . . . . . 28

2.1.4 Orbit Integration . . . . . . . . . . . . . . . . . . . . . 32

2.2 Resultsof the simulation . . . . . . . . . . . . . . . . . . . . . 36

2.2.1 Fra tionof bound neutron stars . . . . . . . . . . . . . 36

2.2.2 Distributionof heights . . . . . . . . . . . . . . . . . . 38

2.2.3 Neutron stars inthe disk . . . . . . . . . . . . . . . . . 40

2.2.4 Mean velo ities . . . . . . . . . . . . . . . . . . . . . . 40

2.2.5 The solar neighbourhood . . . . . . . . . . . . . . . . . 43

2.2.6 Neutron stars inthe halo . . . . . . . . . . . . . . . . . 44

2.2.7 Sky density of neutron stars . . . . . . . . . . . . . . . 44

2.2.8 Results with dierent potential . . . . . . . . . . . . . 48

2.3 Summaryof the results . . . . . . . . . . . . . . . . . . . . . . 48

3 MICROLENSING FROM ISOLATED

NEUTRON STARS AND BLACK HOLES 51

3.2 Basi theory of mi rolensing . . . . . . . . . . . . . . . . . . . 53

3.3 Modelof the Galaxy . . . . . . . . . . . . . . . . . . . . . . . 56

3.3.1 Distributionof normalstars . . . . . . . . . . . . . . . 56

3.3.2 Updated distributionof neutron stars and bla k holes . 57 3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.4.1 Opti aldepth . . . . . . . . . . . . . . . . . . . . . . . 61

3.4.2 Rate of events and distribution of time-s ales . . . . . 62

3.4.3 Comparisonwith previous simulations . . . . . . . . . 70

3.5 Dis ussion of the results . . . . . . . . . . . . . . . . . . . . . 74

4 COUNTERPARTS OF CANDIDATE BLACK HOLE LENSES 77 4.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.1.1 Cataloguesof mi rolensing events . . . . . . . . . . . . 78

4.1.2 Cataloguesof X-ray sour es . . . . . . . . . . . . . . . 79

4.1.3 Cross- orrelationanalysis . . . . . . . . . . . . . . . . 79

4.2 Results of the ross- orrelation . . . . . . . . . . . . . . . . . . 82

4.3 The natureof 2XMM J180540.5-273427 . . . . . . . . . . . . . 87

5 SUMMARY AND CONCLUSIONS 89

A Coe ients of the ts 93

List of publi ations 97

Bibliography 101

The dete tionof oldneutron stars andbla k holes inisolationisone ofthe

ornerstones of ompa t obje t astrophysi s. However, forty years afterthe

rst pioneering studies, no su esful andidates have been found to onrm

the early predi tions, making the sear h for old isolated ompa t obje ts a

stillopenandintriguingsubje t. Thes opeofthisthesisisthustoinvestigate

the observability of isolated neutron stars and bla k holes with the nal

obje tive of dening new possible strategies for the long-sought dete tion of

these elusive obje ts.

The thesis isorganized as follows. In Chapter 1, after ashort dis ussion

on the origin of neutron stars and stellar-mass bla k holes in isolation, I

summarize the results of past eorts made to onstrain their observational

properties.

In Chapter 2 I ta kle with the dynami s of isolated neutron stars. I

des ribe the set-up of a numeri al Monte Carlo ode, named Population

SYnthesis of Compa t Obje ts (PSYCO in brief), developed as part of the

PhD proje t. I then present the results of the simulation, with parti ular

emphasis for statisti alproperties of neutron stars inthe Gala ti disk and

inthesolarneighbourhood. Theserst resultswillbeusedasbasetoexplore

alternative methods to dete t old neutron stars and bla k holes. It should

benotedthat,followingthestandardpra ti e, theserstresultsareobtained

onsideringonly neutronstars born inthe diskof the Milky Way. Asitwill

be shown in Chapter 3, the ontribution of neutron stars, and bla k holes,

born in the Gala ti bulge annot be negle ted sin e they ould represent

the majority of dete table obje ts.

In Chapter 3 the feasibility of mi rolensing as a te hnique to dete t

isolatedneutronstars andbla kholes isexplored,makinguse ofthe results

so far by the several surveys, I des ribe the basi mi rolensing quantities

and expressions. I then des ribe the models adopted in my work for the

distribution of bulge and disk stars, to whi h the ontribution of neutron

stars and bla k holes isthen omparedto. I omparethe opti aldepthand

event rate due to neutron stars and bla k holes with that of normal stars.

Also,I study the distribution of event time-s ales inboth ases.

After theresults reportedin Chapter 3,inChapter 4I present asystem-

ati ross- orrelation analysis of mi rolensing events with the atalogues of

X-ray sour es of the XMM-Newton and Chandra satellites,whi h appeared

re ently. I report the results of the ross- orrelation and the properties of a

sour eresulting fromthe ross- orrelation pro edure.

Finally, in Chapter 5 I review the results of my PhD proje t and draw

the nal on lusion. I alsodis uss possible future developments.

Neutron stars and stellar-mass bla k holes are born mainly in the ore-

ollapse of a massive star, with mass greater than

∼ 8 M

1 M

equal to a solar mass), whi h exhausted its thermonu lear fuel. Hen e, the

star is not able any more to sustain its own gravity and the ore- ollapse

o urs. Thenal out ome ofthis pro essdepends onthephysi alproperties

of the progenitor like, for example, its mass and hemi al omposition (e.g.

Heger et al.,2003).

Neutron stars and bla k holes an be formed also through a retion-

indu ed ollapse of stars in binary systems, (e.g. Lorimer, 2008, and refer-

en es therein). However, the out ome of the ollapseis strongly ae ted by

the omplex intera tions between the two stars in the binary rather than

being dependent only on the initialproperties of the ollapsing stars. Fur-

thermore, the frequen y of a retion-indu ed ollapses is mu h lower than

the ase of isolated massive stars (Arnett et al., 1989). Thus, isolated neu-

tron stars and bla k holes should represent the bulk of the population in

the Milky Way.

1.1 Neutron stars

The formation of a neutron star happens when the pressure of degenerate

neutrons formed by inverse

β

the gravitational for e. The external envelope of the the progenitor star is

theneje ted athighspeed,

∼ 10

km s

Su hevents an be observed even at osmologi al distan es.

After birth, the observational appearan e of neutron stars varies a lot

among single obje ts and it too depends on their intrinsi properties, like

known neutron stars has been dete ted as young isolated pulsars, powered

by magneto-rotationallosses and dete ted through radio or gamma-ray ob-

servations.

The advent of X-ray astronomy allowed the dis overy of other lasses of

isolated neutron stars that are not shining at radio or gamma-ray wave-

lengths. In these obje ts the emission omes from the dissipation of the

magneti eld and/orresidual heatasinmagnetars orinXDINS and CCOs

(X-ray Dim Isolated Neutron Stars and Central Compa t Obje ts respe -

tively,see e.g. Mereghetti 2008; Turolla 2009 for reviews).

Anyway, whateverthe natureof their energy reservoir is,the emissionof

isolatedneutron stars isexpe tedtofadeaway inatime-s alemu h shorter

than the age of the Milky Way, whi h is

∼ 10

. 10

likely produ ed su h massive stars throughout its existen e, alarge number

of exhausted neutron stars isthus expe ted to beharboured init.

Fromestimates ofnu leosynthesis yieldsby ore- ollapsesupernovae, Ar-

nettetal. arguedthatasmanyas

∼ 10

inourGalaxy,thelargemajorityleavinganeutronstar asremnant(Fig. 1).

However, a more re ent estimate of the ore- ollapse rate was obtained by

Diehletal.(2006) frommeasurementsof the gamma-rayemissionof

26

Al

the interstellarmedium,and returned a value of

∼ 2

pliesthat, assuminga onstantstar formationrate throughoutthe existen e

of the Galaxy,

∼ 2 × 10

bla kholes(dottedlines). Dierentlinestylesrepresentdierentinitialmass

fun tions. Sour e: Heger etal. (2003).

Stellar-mass bla k holes are the nal evolutionary phase of very massive

stars. Stars with initial mass

M & 40 M

ollapse into a bla k hole, without generating a supernova. However, bla k

holes ouldformalsoby a retionoffall-ba kmaterialontoanew-bornneu-

tron star, if the mass of the progenitor is inthe range

25 M

. M . 40 M

(Heger et al., 2003). Furthermore, the omposition of the progenitor plays

animportantrole: for metalli itiesabove the solar one, the amountof mass

lost through stellar wind an be so large that even the most massive stars

end their lives as neutron stars ratherthan leavinga bla k hole as remnant

(Figure2). This s enariohas possibly been onrmed by the dete tion of a

magnetar, CXO J164710.2-455216, asso iated with the massive star luster

Westerlund 1. Theturn-opointofthe lusterisaround

∼ 35 M

thattheinitialmass oftheprogenitorofCXOJ164710.2-455216shouldhave

been

& 40 M

Nevertheless, a rude estimateof the number of Gala ti bla k holes an

beobtainedfromthestellarinitialmassfun tion(e.g.Salpeter,1955;Kroupa,

2001): the ratio between the number of bla k holes and neutron stars is

∼ 0.1 − 0.2

times

10

∼ 10

1.3 The past 40 years

The dete tion of this large populationof oldneutron stars and stellar-mass

bla k holes inisolation would be of paramount importan e. Their distribu-

tion in phase-spa e ould, for example, a t as a probe of the gravitational

potentialofthe MilkyWay,aswellastogivepre ious insightsonthemagni-

direct black hole

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BH by fallback

BH by fallback

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neutron star

neutron star

BH by fallback (weak SN)

BH by fallback (weak SN)

iron core collapse

O/Ne/Mg core collapse

low mass stars −− white dwarfs

direct black hole

direct black hole

direct black hole

no H envelope

25 40 60 100 140

initial mass (solar masses) 9 10

about solarmetal−free

34 260

metallicity (roughly logarithmic scale)

Figure2: Remnantsof singlemassivestars asa fun tionofthe initialmetal-

li ity (y-axis)and initialmass (x-axis). Sour e: Heger et al.(2003)

at birth. This fa t may itself help to onstrain the physi al me hanism re-

sponsiblefortheseki ks. Usefulinformationaboutthestarformationhistory

of the Milky Way ould be alsoretrieved.

The sear h for old neutron stars and bla k holes in isolation has been

ta kledbymanyauthorsinthepast. Ostrikeretal.(1970)proposedthatold

neutron stars ould be re y led by a retion from the interstellar medium,

under the hypothesis of spheri al a retion (Bondi & Hoyle, 1944; Bondi,

1952). Assuming a velo ity with respe t to the medium

v ∼ 10 km s

density of the medium

n ∼ 1 cm

M = 1.4 M

and

R = 10

cm

L = G M ˙ M

R ∼ 2 × 10

 M ˙ 10

g s

 erg s

,

where

M = ˙ 2π(GM)

m

n

(v

+ c

)

∼ 10

nv

g s

,

is the a retion rate a ording to the Bondi-Hoyle-Littleton theory,

m

the mass of the proton,

c

v

= (v

+ c

)

/(10 km s

)

kT

would be

∼ 100 eV

The laun h of the ROSAT satellite, with its good sensitivity in the soft

X-ray band, gave boost to the sear h of isolated neutron stars and bla k

holes, espe ially the former sin e, being more numerous than bla k holes,

results of numeri al simulation of Pa zynski (1990), Treves & Colpi (1991)

predi ted the hundreds to thousands a reting old neutron stars would be

potentiallyobservablebyROSAT. Similarpredi tionswere madebyBlaes&

Madau (1993). However, onlya handful of isolated neutron stars have been

dis overed by ROSAT(e.g. Walter&Matthews 1997). These are ommonly

a epted as middle-aged ooling neutron star, the aforementioned XDINS,

likelybornin lose-bystar-formingregions(Popov etal.,2005;Posseltetal.,

2008).

Theoreti al models of a retion from the interstellar medium have been

developedinasimilarfashionalsoforbla kholes(seee.g.Campana&Pardi,

1993; Agol & Kamionkowski, 2002; Beskin & Karpov, 2005; Mapelli et al.,

2006). However, predi tions for bla k holes are ai ted by larger un er-

tainties sin e the only useful information about their statisti al properties

derives from few known obje ts in X-ray binaries. On the other hand, the

phase-spa e distributionof isolatedbla k holes is ompletelyun onstrained.

Thela kofisolateda retingneutronstarsandbla kholes(e.g. Neuhäuser

& Trümper 1999) has more than one possible explanation. First, the spher-

i ala retion rate is strongly dependent of the relativevelo ity between the

a reting obje t and the surrounding medium ( fr. Equation 1.2). Popov

et al. (2000) explored the observability of a reting old neutron stars for a

wide range of initialmean velo ities, between 0 and 550

km s

Maxwellian distribution. The observed pau ity of a retors in the ROSAT

ataloguewouldbeexplainedifneutronstarsarebornwithaveragevelo ities

ofatleast

200 km s

∼ 10

of normal stars in the Gala ti disk. Therefore the a retion rate would be

afa tor

∼ 10

− 10

the propermotionsof known young neutron stars (see Chapter 2).

Se ond, neutron stars are born with very strong magneti elds,

B ∼ 10

− 10

G

P ∼ 30 − 100 ms

put stringent onstraints on the onditions for whi h the a retion ow an

penetratethemagnetosphereoftheneutronstar(seee.g.Trevesetal.,2000).

The rst ondition is that the

Alfv´en

the dynami s of the infallingmatter is dominated by the magneti eld (Il-

larionov & Sunyaev, 1975)

r

=  B

R

√ 2GM ˙ M



(1.3)

∼ 2 × 10

 B 10

G



 M ˙ 10

g s



 R 10

cm



 M M



cm ,

must be smaller of the a retion radius

r

= 2GM

v

∼ 3 × 10

 M M

 v

cm ,

whi h denes the region where the dynami s of the interstellar medium is

dominated by the gravitationaleld of the neutron star. The se ond ondi-

tion isthat the gravitational energy density of the infallingmatterat a re-

tion radius

U

= GMm

n

r ∼ 6.5 × 10

 M ˙ 10

g s

 r 10

cm



erg cm

,

dipoleradiation

U

=  B

8π

 R

r

 r

r



(1.6)

∼ 7.5 × 10

 B 10

G



P

 r 10

cm



ergcm

,

where

r

= cP/2π

onthe spin period,whi hmust be larger than a riti al value

P & P

∼ 10  B 10

G



 M ˙ 10

g s



 r

10

cm

 R 10

cm



 M M



s .

As Blaes & Madau have pointed out, the time-s ale ne essary for an

isolated neutron star to slow down its rotation to

P & P

order of the age of the Galaxy. This would mean that in many ases the

onditionsfor a retion ouldbehardly rea hedduringthe neutronstar life.

Furthermore,even if

P > P

Alfv´en

 GM r



&  2π P



r

.

This fa t puts another stronger onstrainton the spin period