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Radiation efficiencies of the pulsars detected in the optical range 5 0 Zharikov S.a, Shibanov Yu.b, Komarova V.c 0 2 aOAN IA UNAM, Ensenada, BC, Mexico n a J bIoffe Physical Technical Inst, RAS, St. Petersburg, Russia 0 1 cSpecial Astrophysical Observatory, RAS, Russia 3 v Using available multiwavelength data for the pulsars of different ages detected in the optical 2 range, we analyze the efficiencies of the conversion of the pulsar spindown power E˙ into the 5 1 observednon-thermalluminosityLindifferentspectraldomains. Wefindthatthesepulsarsshow 0 significantly non-monotonic dependencies of the optical and X-ray efficiencies (η =L/E˙) versus 1 pulsar age with a pronounced minimum at the beginning of the middle-age epoch (∼ 104 yr) 4 0 and comparably higher efficiencies of younger and older pulsars. In addition, we find a strong / correlation between the optical and 2–10 keV X-ray luminosities of these pulsars that implies h p the same origin of their nonthermal emission in both spectral domains. - o r st 1. Introduction I ≈ 1.1×1045 gm cm2 is the inertia mo- a mentum of a NS of 1.4 M and 10 km : ⊙ v The properties of the observed pulsar ˙ radius, P and P are the pulsar period and i X emission show that radio and gamma-ray itsderivative, respectively. E˙ isfrequently r photons have nonthermal origin and are called also the spindown luminosity and a produced by relativistic particles in dif- denotedasL . Theratioη = L/E˙, where sd ferent parts of the pulsar magnetosphere. Listhephotonluminosity, isusedtochar- The soft X-ray-optical radiation can be a acterize the efficiency of the conversion of combination of several nonthermal spec- E˙ ≡ L into the pulsar emission at a sd tral components from the magnetosphere given spectral domain. In this paper, we and thermal components from the whole analyze the evolution of the nonthermal surface of a cooling neutron star (NS) luminosities and efficiencies of pulsars de- and from its hot polar caps heated by tected in the optical range. Such analy- the relativistic particles from the magne- sis has been performed about 10 yr ago tosphere. The nonthermal component has in pioneering works [1,2]. However, con- been found to dominate the optical emis- siderable progress in the pulsar distance sion of several young, middle-aged, and measurements, and much higher quality old pulsars. It is believed that nonther- of recent optical and X-ray observations mal components are powered by NS rota- allowing to resolve better the nonthermal tional energy loss E˙ = 4π2IP˙/P3, where and thermal emission components from 1 2 S. Zharikov, Yu. Shibanov, V. Komarova Table 1 The dynamical ages τ = P/2P˙, distances d, spindown luminosities E˙ (or L ), and ob- sd served nonthermal luminosities in the radio, L , optical, L , X-rays, L , and gamma- R Opt X rays, L , of seven radio pulsars detected in the optical range [4,5]. Figures in brackets are γ ±1σ uncertainties of the values. Source log τ d log E˙ log L a log L log L log L R Opt X γ [yr] [pc] [erg s−1] [mJy kpc2] [erg s−1] [erg s−1] [erg s−1] 408 MHz B band 2-10 keV ≥400MeV Crab 3.1 2.0×103 38.65 3.41(4) 33.23(5) 36.67(+20) 35.7(+1) −26 −3 B0540-69 3.2 5.0×104 38.17 3.30(9) 33.47(15) 36.99(+19) ≤ 35.97 −23 Vela 4.1 293(+19) 36.84 2.64(20) 28.3(3) 31.2(+36)i 33.9(+1) −17 −38 −3 B0656+14 5.0 288(+33) 34.58 -0.27(9) 27.53(8) 30.30(+36) 32.37(+10) −27 −28 −30 Geminga 5.5 153(+59) 34.51 0.375(+27) 26.95(+16) 29.35(+38) 32.95(+10) −34 −23 −10 −36 −30 B1929+10 6.5 36110 33.59 1.52(5) 27.26(+20) 29.86(+13) ≤ 32.57 −8 −33 −15 B0950+08 7.2 262(5) 32.75 1.44(16) 26.88(8) 29.28(+13) ≤ 32.51 −18 a 2 2 The radio luminosity is defined traditionally as LR =S408d1 [mJy kpc ], where S408 is the observed flux density from a pulsar at 408 MHz in mJy, and d1 is its distance in kpc. At a typical radio band FWHM of about 100 kHz the conversion factor to standard luminosity units is ≈9.51×1021 [erg s−1]/[mJy kpc2]. the pulsars and to identify in these ranges optical pulsars are much less certain and several new objects enable us to update we excluded them from consideration. In significantly previous analysis and to get the optical we used the data obtained in qualitatively new results on the evolution the B-band [4,5] since practically all the of old pulsars. pulsars from our sample were detected in this band and fluxes in other bands are 2. The sample and data sources not strongly different from these. Using this band also allows us to escape possi- Wehaveanalyzedmultiwavelengthnon- ble contamination of the pulsar fluxes by thermal luminosities of seven pulsars de- strong nebular lines in cases when an as- tected in the optical range (see Table 1; sociated nebula around a pulsar exists, or [4,5]). The advantage of this sample is a is expected to exit. In X-rays we used small (<10%) uncertainty in the distances the data obtained in 2-10 keV range [6,5], to the pulsars, determined from the radio where the nonthermal power law spectral or optical parallax measurements. This tails dominate over the thermal compo- strongly minimizes errors in the inferred nents detected from several pulsars in a luminosities. Distances for a few other Radiation efficiencies of the pulsars. 3 Log Lsd333693 CrabJ0540 Vela B0656 Geminga B1929 B0950 ---222687 Log ηR = −38.216(341) + 1.183(051) log τ -29 Log LR 02 ηLog R--3301 -32 ηLog R-33 --3343 -36 -35 Log LOpt3228 -36 from Zavlin&Pavlov (2004) ηLog Opt --68 0 ffffrooitorr fm PPo SSrP RRηoRsss swweniittthhi elloot gga lττ. (><2 0550..552) without MSPs Log LX3326 ηLog X-2 -0.96 1.08 -4 ηLog X --42 -6 36 -6 1.18 Log Lγ 3324 3 4 5 Log τ 6(yrs) 7 8 9 0 ηLog γ -2 Figure 2. Top: radio efficiencies of 500 pulsars from ATNF [8] vs dynamical age; 3 4 5 6 7 Log τ [ yr ] triangles mark the pulsars with more ac- Figure 1. From top to bottom: evolution curateparallax-baseddistancesandcircles of the pulsar spindown, radio, optical, X- select optical pulsars from Table 1. Bot- ray, and gamma-ray luminosities and re- tom: X-ray efficiencies vs dynamical age; spective efficiencies, with dynamical age. lines are the linear regression fits of evo- Filled circles are the data taken from [7]. lution tracks of younger and older pulsars Hereafter errorbars and arrows show ±1σ and numbers show the line slopes. value uncertainties and 1σ upper limits, respectively. softer energy range. We added also the 3. Results data from [7] on 5 old pulsars recently ob- 3.1. Evolution served with the Chandra and XMM. In The nonthermal luminosity and effi- the radio and gamma-rays we used the ciency evolution of pulsars in different data obtained at 400 MHz (ATNF catalog spectral domains, based on the selected [8]) and in the EGRET range of 400 MeV- sample of the optical pulsars, is shown in 10 GeV [9], respectively. Here we con- Fig. 1. We note the following points: sider only isotropic equivalents of the lu- (1) the spindown luminosity decreases minosities neglecting the emission beam- monotonically with age, as expected from ing which is not yet properly known in the a formal dependence E˙ ∼ τ−1P−2 and all considered ranges for all our objects. 4 S. Zharikov, Yu. Shibanov, V. Komarova tonic decrease of the efficiency with age -1 suggested by [2] through lack of data on -2 η (2-10 keV)Log X--43 1.19(13) oorrealfdmdtihaoperukadlansebadprlyesgnasadmitmemnticlhaaiae-rrtsatηytoiompeetffia(eτc;ch)i(ea5onn)tchditeehsηre;Xin((s6cτhr))aeptaahsereees -5 with age but their increases becomes ap- -6 parentlysteeperfromthesamemiddle-age -9 -8 -7 -6 -5 Log η (B-band) epoch. Opt Figure 3. Relationship between the opti- The fact that older pulsars are much cal and X-ray efficiencies in the B band more efficient radio emitters than younger and 2-10 keV ranges. ones is confirmed at a much higher signifi- cance level based on a rich sample of radio -1 pulsars extracted from the ATNF catalog -1.5 (Fig.2,toppanel). Thescatterofthedata -2 (Β)(2-10)Log L / LxOpt--32-..355 atbhlyoisndgpiffatenhreeelnmbtyegaesnoolmeidveotllriunicteaiolm/nbateyraambcekinesgxhpoflawacintnoeirdns and uncertainties in the distance. The -4 pulsars with parallax based distances are -4.5 generally below this line. This may re- -5 2 3 4 5 6 7 8 Log τ (yrs) flect a systematic shift between the paral- Figure 4. The evolution of the optical and lax and dispersion measure distances used X-ray luminosities ratio with dynamical for the rest objects. age. The nonmonotonic efficiency evolution in X-rays becomes much less obvious if longer periods of older pulsars; (2) the we consider a larger sample of pulsars optical, X-ray and gamma-ray luminosi- identified in X-rays including a few of ties also decrease with age, but become them identified in the optical and X-rays almost constant starting from a middle- (Fig. 2. low panel). The statistics is much age epoch of 104 − 105 yr; (3) the ra- poor than in the radio and this picture is dio luminosity is less monotonic but starts more affected by the distance and flux un- to increase gradually approximately from certainties. Nevertheless, applying linear the same age; (4) as a result, the evolu- regression fits separately to sub-samples tion of the optical and X-ray efficiencies is of sub-middle-aged and post-middle-aged non-monotonic and shows a pronounced pulsars, one can resolve hints of the non- minimum efficiency at a middle-age epoch monotonic evolution clearly seen in the of 104 −107 years and comparable higher optical sub-sample. In the example shown efficiencies for younger and older pulsars in Fig.2, (low panel) the Geminga age of in contrast to the conception of a mono- Radiation efficiencies of the pulsars. 5 105.5 yr, when the optical efficiency start to increase, was used to divide by sub- ηog R--3342 -0.55(18) η~ Lsd-1/2 samples. In this case the evolution track L -36 -0.89(35) of older pulsars may be compatible with what is seen in the radio range(cf. dashed Opt -6 η and solid lines). Using other dividing ages Log -8 0.16(24) -0.65(10) from the range of the middle-aged epoch -10 of 104−106 yr does not change the picture -2 X η qualitatively though slopes values can be g -4 o different, buttheyarealwaysnegativeand L -6 0.34(27) -0.55(15) positive for younger and older pulsars, re- 0 spectively. In all of the X-ray plots we ηγ added X-ray data for 5 old pulsars de- Log -2 -0.29(12) -0.47(23) -4 tected recently with Chandra and XMM 32 34 36 38 [7]. These data are likely to be consistent Log L [erg s-1] sd with the proposed evolution picture. To Figure 5. From top to bottom: relation- confirm or reject it better quality X-ray ships between the efficiencies in the radio, data and distance information are needed. optical, X-ray, and γ-rayspectral domains and spindown luminosity. Different pul- 3.2. Correlation between the optical sars are denoted by the same symbols, as and X-ray emission in Fig. 1. Dashed and solid lines show the Similar shapes of the optical and X-ray best linear regression fits of the whole set evolution tracks suggest a correlation be- of pulsars, and without the two younger tween the luminosities in these domains. ones (Crab and PSR B0540-69, with the This is confirmed by the linear regression highest L ), respectively. The slope val- sd fit of the η vs η distribution shown in opt X ues are indicated near the lines. Dotted Fig. 3. The correlation coefficient is 0.97. lines indicate a slope in case of the linear A strong correlation implies the same ori- proportionality of the luminosity to the gin for the emission in both spectral do- Goldreich-Julian current [3]. mains. It is independent of the differ- ence in the spectral slopes in these ranges becomes almost independent of age start- observed for the pulsars of different age. ing from a middle-age epoch. Forinstance, theextrapolationofthenon- thermalcomponent of theX-ray spectrum 3.3. The efficiency and the spindown of young Crab-like pulsars strongly over- luminosity shoots the observed optical fluxes, while The distributions of the efficiencies of forolderpulsars theopticalfluxes aregen- theopticalpulsars indifferent spectral do- erallycompatible withsuch extrapolation. mains vs spindown luminosity are shown This is reflected in the evolution of the ra- inFig.5. These distributionsdemonstrate tio L /L shown in Fig. 4. The ratio that: (1) in the radio and gamma-rays, opt X 6 S. Zharikov, Yu. Shibanov, V. Komarova As in case of the evolution picture, --2267 LR ~ Const Log ηR = −3.367(924) − 0.83(03) log Lsd the fact that the pulsars with lower Lsd --2298 LR ~ Lsd0.2 are more effective radio emitters is firmly confirmed by the analysis of a much -30 η Log R--3321 ltahregeArTsNaFmpclaetaolofgp[u8l]sa(Frsige.x6t,ratoctpedpafnreolm). -33 Comparing the triangles and black point -34 -35 distributions in Fig. 6, (top panel), we -36 can note that the scatter around an av- 0 ffrroomm ZPoavsslienn&ti Peat vallo. v(2 (020020)4 w)ithout MSPs erage distribution shown by the solid line ffoorr PPSSRRss wwiitthh LLssdd <> 3344..55 is likely equally caused by uncertainties in -2 0.5 the pulsar geometry (triangle points), and ηLog X -0.83 DM-based distances (black points). The -4 slope of the distribution is different from -1.20 atrivialoneassumingL ∼ const (dashed R -6 line in this plot) but suggests an increase 28 29 30 31 32 33 34 35 36 37 38 39 of the radio luminosity ∝ L0.2. Log L (erg s-1) sd sd The separation into two sub-classes of Figure 6. Top: radio efficiencies of 500 thelowandhighspindownluminositypul- pulsars from ATNF database [8] vs L ; sars that is clearly seen in the middle sd notations are the same as in Fig. 2. Bot- panels of Fig. 5 for the optical pulsars tom: X-ray efficiencies vs spin-down lumi- is not obvious for a wider sample of pul- nosity; lines fit the distribution of lower sars identified in X-rays (Fig. 6, bottom and higher L pulsars; numbers show the panel). The reasons are likely to be the sd line slopes. same as we have mentioned in Sect. 3.2 (poor statistics + distance and flux un- less energetic pulsars (with low Lsd) are certainties). However, as in the case of more efficient photon emitters than more the evolution picture for the same sample energetic ones; (2) in these ranges the ef- shown inFig.3, linear regression fits allow ficiency increases monotonically with the us to resolve a hint of a bimodal distribu- Lsd decrease; (3) the same is seen in the tion with the efficiency increases toward optical and X-ray ranges with an exclu- the low and high sides of the considered sion of the two most energetic and young L range. The bottom panel of Fig. 6, sd pulsars, Crab and PSR B0540-69, which where L of Geminga was used, as in case sd form a separate sub-class in these distri- of Fig. 3, to divide the pulsars by sub- butions; (4) recent data for the five old samples, suggests also that the distribu- pulsars identified in X-rays (filled circles tion of the low L pulsars may be roughly sd in Fig. 5) do not change the above ten- compatible with what is seen in the radio dency in X-rays and may even strengthen range (cf. solid and dashed lines in this it (cf. Fig. 6, bottom panel). Radiation efficiencies of the pulsars. 7 plot). The suggested bimodal distribution can hardly be explained by geometry ef- This work has been partially sup- fects, if we compare the relatively small ported by CONACYT project 36585-E, scattering of the triangle points around a and RFBR grants 02-02-17668, 03-02- meandistributionintheradio(toppanel), 17423, 03-07-90200and RLSS 1115.2003.2 likely caused by geometry effects, and the much larger scattering of all points in X- REFERENCES rays (bottom panel). 1. Mereghetti, S.; Caraveo, P. A.; Big- nami, G., Multiwavelength observa- 4. Summary tions of isolated neutron stars, ApJS Our multiwavelength analysis of the 92, 521-526, 1994 nonthermal luminosity and efficiency dis- 2. GoldoniP., Musso, C., Caraveo, P.A., tributions vs dynamical age and spin- et al.,Multiwavelength phenomenol- down power of the pulsars detected in the ogy of isolated neutron stars, A&A, optical range suggests significantly non- 298, 535-543, 1995 monotonic evolution of their emission in 3. 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