PSR J1840−1419: A VERY COOL NEUTRON STAR

E. F. Keane; M. A. McLaughlin; M. Kramer; B. W. Stappers; C. G. Bassa; M. B. Purver; P. Weltevrede

doi:10.1088/0004-637X/764/2/180

1. INTRODUCTION

Measurements of the temperatures of neutron stars (NSs) are few and far between. They are often impossible as, for ages ≳ 1 Myr, the star will have experienced significant cooling since its formation (Yakovlev & Pethick 2004). The thermal emission from NSs peaks in soft X-rays, below ∼1 keV, and the luminosities are such that sources even a few kiloparsecs away are difficult to detect. Currently, a total of 37 measurements, and 9 upper-limit measurements, of rotation-driven NS temperatures have been published (Li et al. 2005; Caraveo et al. 2010; Abdo et al. 2010; Speagle et al. 2011; Chang et al. 2012; Zhu et al. 2011; Marelli et al. 2011; Guver et al. 2012; Pires et al. 2012). Of these, only 11 are for NSs with characteristic ages older than 1 Myr (excluding 5 millisecond pulsars for whom we have no meaningful estimate of age), and only 3 of those greater than 10 Myr: PSRs B0950+08, J2144−3933, and J0108−1431. The emission from PSR B0950+08, a 17.5 Myr pulsar, is non-thermal, with a power-law spectrum and an upper limit of kT^∞_bb < 41 eV, or T < 0.48 MK, on the thermal contribution (Becker et al. 2004). To put this in context, it is at the level of the lowest measured temperature for any NS: kT^∞_bb = 43 eV for Geminga (De Luca et al. 2005). PSR J2144−3933 is the slowest spinning pulsar known (P = 8.5 s) and an order of magnitude older (272 Myr) than PSR B0950+08 so that it is perhaps not surprising that no X-ray emission has been seen from it, with an upper limit of kT^∞_bb < 20 eV (Tiengo et al. 2011). Posselt et al. (2012) have recently reported the detection of PSR J0108−1431 (170 Myr) with kT^∞_bb = 110 eV, a source that seems to be undergoing a heating process.

In a recent re-analysis of the Parkes Multi-beam Pulsar Survey, PSR J1840−1419 was discovered (Keane et al. 2010). This 6.6 s pulsar shows sporadic radio emission with strong single pulses detected, on average, every ∼10 rotation periods, at flux densities up to 1.7 Jy. At 16.5 Myr, PSR J1840−1419 has a very similar characteristic age to PSR B0950+08, and therefore might be expected to have somewhat similar X-ray properties. This, plus its relative proximity at 850 pc, make PSR J1840−1419 an excellent target for adding to our knowledge of the X-ray emission and temperature of old NSs. In this paper we present the result of a Chandra observation of PSR J1840−1419.

One factor that has been suggested to be a major factor in NS cooling is the magnetic field strength. Several authors have suggested that NSs with higher magnetic field strengths are hotter than those with lower field strengths for the same age (Gonzalez et al. 2007; Zhu et al. 2009, 2011; Olausen et al. 2010). Such an effect is theoretically predicted (Yakovlev & Pethick 2004) and the work of Geppert et al. (2004) and Pérez-Azorín et al. (2006) shows that high magnetic fields suppress heat conductivity perpendicular to the field lines, naturally producing an anisotropic temperature distribution on the stellar surface with small hot regions at the magnetic poles. We examine this claim with XMM-Newton observations of two pulsars: J1814−1744 and J1847−0130, both of which have high magnetic field strengths of 5.5 × 10¹³ and 9.4 × 10¹³ G, respectively.

Finally, we present an updated plot of kT^∞_bb versus characteristic age for all X-ray measurements of, and upper limits on, rotation-powered NS temperature made thus far, and re-examine the temperature–magnetic field strength relationship.

2. OBSERVATIONS AND RESULTS

2.1. Calculating Limits

For a non-detection, one could determine a count rate limit by following the procedure of Pivovaroff et al. (2000): (1) define an aperture on the image about the position of the source, and add up the counts in this region, N; (2) define a background region of the same area (or appropriately scale to the same area) elsewhere on the image and add up the counts in the background region, B. The signal from the source is N − B and the noise is $\sqrt{N+B}$ . The signal-to-noise ratio is then $(N-B)/\sqrt{N+B}$ . To set a "3σ limit" count rate we can then solve for N in 9(N + B) = (N − B)², where B is known. We can see that in the N ≫ B "photon-rich" case this tends to the expected Poisson value in the absence of background sky noise. However, in the "photon-poor" case we clearly cannot use this expression, e.g., for B = 0.35, N = 10 naively suggests a 99.7% detection/limit; however, we know that the Poisson probability for 10 counts due to noise is ≈10⁻¹³%; for such a background rate three counts represents a 99.8% limit. The observations presented here are in the photon-poor scenario, so that using the Pivovaroff et al. (2000) procedure would result in a much poorer limit than what has truly been obtained.

To convert count rate limits to flux limits we need either some kind of absolute scale, e.g., from observing a standard source of known flux, or a model for our source, e.g., an assumed spectral form (McLaughlin et al. 2003). Below we calculate one set of limits for a blackbody model (whence we obtain temperature limits as a function of the emitting radius), and another set of limits for a non-thermal model with a power law with negative index of 2.0.

2.2. PSR J1840−1419

PSR J1840−1419 is an old pulsar (16.5 Myr) with a 6.6 s spin period. Due to its sporadic radio emission, it was detected in a search for single pulses rather than in a periodicity search (Keane et al. 2010). Pulsars discovered in this way are often referred to as "RRATs" (Keane & McLaughlin 2011). The properties of PSR J1840−1419, both measured and derived, are given in Table 1.

Table 1. Measured and Derived Properties and Limits for Three Pulsars

Quantity	J1840−1419	J1814−1744	J1847−0130
P (s)	6.6	4.0	6.7
$\dot{P}$ (fs s⁻¹)	6.3	745	1270
τ_c (kyr)	16500	85	83
B (10¹² G)	6.5	55.1	93.6
$\dot{E}$ (10³⁰ erg s⁻¹)	1.0	468	167
DM (cm⁻³ pc)	19	792	667
D (kpc)	0.9	9.8	7.7
Telescope	Chandra	XMM	XMM
Instrument	ACIS-S	PN	PN
Date	2011 Feb 20	2004 Oct 21	2004 Sept 14
Energy range (keV)	0.2–10	0.15–15	0.15–15
T_obs (ks)	10.0	6.1	17.0
N_H (10²⁰ cm⁻²)	6	157	205
kT^∞_bb (eV)^a	<24⁺¹⁷₋₁₀	<123⁺²⁰₋₃₄	<115⁺¹⁶₋₃₃
T^∞_bb (MK)^a	<0.28^+0.19_−0.12	<1.42^+0.22_−0.39	<1.33^+0.19_−0.38
f_bb (10⁻¹⁴ erg cm⁻² s⁻¹)^b	<5.0	<6.1	<8.9
L_bb (10³⁰ erg s⁻¹)^b	<4.3	<692	<640
f_nt (10¹⁵ erg cm⁻² s⁻¹)	<3.0	<8.9	<5.1
L_nt (10³⁰ erg s⁻¹)	<0.26	<102	<36
$\eta =L_{{\rm nt}}/\dot{E}$	<0.26	<0.22	<0.22

Notes. The measured and derived properties for the three pulsars discussed in this paper. The spin period, P, and its derivative, $\dot{P}$ , are derived from pulsar timing techniques, and τ, B, and $\dot{E}$ , the characteristic age, magnetic field strength, and spin-down energy, respectively, are inferred from these (Keane et al. 2011). The distance, D, is derived from the measured DM using the NE2001 model for the Galactic free electron distribution (Cordes & Lazio 2002). The 99% confidence temperature limits are derived as outlined in the text. Non-thermal flux limits are given for a power law with negative index of 2.0. ^aThese limits are for an emitting radius of 10 km, and scale as (R^∞_bb/10 km)^α, where α equals −0.39, −0.23, and −0.21, respectively, for the three sources (see main text). ^bThe blackbody flux and luminosity limits similarly scale as (R^∞_bb/10 km)^{2 − α}.

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On 2011 February 20, we performed a 10 ks observation of PSR J1840−1419, using the ACIS-S detector on Chandra in the energy range 0.2–10.0 keV. We detected only one photon within the ∼1'' (3 pixel) error circle of the position derived from pulsar timing (Keane et al. 2011). Assuming that this one count is consistent with background noise (the background rate being 0.24 counts pixel⁻¹), and ignoring the Poisson nature of the source, the count rate limit is 3 × 10⁻⁴ counts s⁻¹ (at 99% confidence).

In the case of a blackbody model this count rate limit implies a temperature limit of kT^∞_bb < 24⁺¹⁷₋₁₀ eV(R^∞_bb/10 km)^−0.39, where the dependence on R^∞_bb is a purely empirical fit to a simple power law of the form T₁₀R^α₁₀, where R₁₀ is the blackbody radius in units of 10 km and T₁₀ is the temperature when R₁₀ = 1: see the top left panel of Figure 1. The error bars reflect both NE2001 "worst case" errors of a factor of two in the distance (Cordes & Lazio 2002) as well as factor of two uncertainties in the neutral hydrogen column density (see below). The bottom right panel of Figure 1 shows all measured NS temperatures as a function of age. The PSR J1840−1419 limit is amongst the coolest of all published limits. The corresponding flux and luminosity limits are f_bb < 5.0 × 10⁻¹⁴(R^∞_bb/10 km)^1.61 erg s⁻¹ cm⁻² and L^∞_bb < 4.3 × 10³⁰(R_bb^∞/10 km)^1.61 erg s⁻¹, respectively. In the case of the non-thermal model (power law, with negative index of 2.0), the flux and luminosity limits are f_nt < 3.0 × 10⁻¹⁵ erg s⁻¹ cm⁻² and L^∞_nt < 2.6 × 10²⁹ erg s⁻¹, respectively.

**Figure 1.** The first three plots show the temperature limit (i.e., which produces the observed count rate limit for an assumed blackbody model) as a function of the assumed emitting radius for the *Chandra* observation of PSR J1840−1419 (10 ks) and the *XMM-Newton* observations of PSRs J1814−1744 (6 ks) and J1847−0130 (17 ks). The points are fit with a simple power law of the form T₁₀(R₁₀)^α. In each case the middle curve is for the nominal dispersion-measure-derived distance. The cooler and hotter curves are for "worst-case" distance errors of a factor of 2 (Cordes & Lazio 2002). For clarity of presentation, we show here only the curves for the nominal N_H values quoted in Table 1. The fourth plot shows all known temperature values as a function of characteristic age. Sources with inferred magnetic field strengths ⩾10¹³ G are marked in blue, whereas those with lower values are marked in black. The open circles denote the upper limits. The three upper limit presented in this paper are marked with large circles for clarity. Note that the symbols for PSRs J1814−1744 and J1847−0130 are largely overlapping as their ages and derived limits are very similar.
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The above estimates use a neutral hydrogen column density of N_H = 6 × 10²⁰ cm⁻², which is derived from the dispersion measure, assuming 10 neutral hydrogen atoms per free electron (Seon & Edelstein 1998). The predicted count levels were calculated using the standard PIMMS (Portable, Interactive Multi-Mission Simulator) tool.⁴

2.3. PSRs J1814−1744 and J1847−0130

We also present the results of two XMM-Newton observations using the PN detector and medium filter in the energy range 0.15–15.0 keV. PSR J1814−1744 was observed for 6.1 ks on 2004 October 21, and PSR J1847−0130 was observed for 17.0 ks on 2004 September 14. The observations of these young, high-B pulsars also resulted in non-detections. As above for PSR J1840−1419, we derive temperature upper limits for these sources of kT^∞_bb < 123⁺²⁰₋₃₄ eV(R^∞_bb/10 km)^−0.23 for PSR J1814−0130, and kT^∞_bb < 115⁺¹⁶₋₃₃eV(R^∞_bb/10 km)^−0.21 for PSR J1847−0130 (see Figure 1). These limits are much less constraining given the much larger estimated distances (7.7 and 9.8 kpc, respectively). The associated flux and luminosity limits for the blackbody scenario are f_bb < 2.6 × 10⁻¹³(R^∞_bb/10 km)^1.77 erg s⁻¹ cm⁻² and L^∞_bb < 3.0 × 10³³(R_bb^∞/10 km)^1.77 erg s⁻¹ for PSR J1814−1744, and f_bb < 3.2 × 10⁻¹³(R^∞_bb/10 km)^1.79 erg s⁻¹ cm⁻² and L^∞_bb < 2.3 × 10³³(R_bb^∞/10 km)^1.79 erg s⁻¹ for PSR J1847−0130.

The non-thermal limits are f_nt < 8.9 × 10⁻¹⁵ erg s⁻¹ cm⁻² and L^∞_nt < 1.0 × 10³² erg s⁻¹ for PSR J1814−1744, and f_nt < 5.1 × 10⁻¹⁵ erg s⁻¹ cm⁻² and L^∞_nt < 3.6 × 10³¹ erg s⁻¹ for PSR J1847−0130. For PSR J1814−1744 the value of N_H derived from the dispersion measure was ∼50% higher than the maximum Galactic value for this line of sight, as calculated by the standard COLDEN tool,⁵ so the COLDEN value of N_H = 1.6 × 10²² cm⁻² was used. For this reason N_H is unlikely to be underestimated, but we have allowed for the possibility that it may be overestimated by as much as a factor of two. Likewise, for PSR J1847−0130, the neutral hydrogen column density was derived to be N_H = 2.1 × 10²² cm⁻². This value of N_H is very close to the maximum value for this line of sight, so that it too is unlikely to be an overestimate.

3. DISCUSSION AND CONCLUSIONS

Although this paper reports three null results, we deem it to be of the utmost importance to report such investigations to avoid duplicated efforts, wasted telescope resources, etc. Table 1 summarizes the temperature, flux, and luminosity limits for the sources reported here. From the non-thermal luminosity limits we can determine upper limits on the non-thermal X-ray efficiency, $\eta =L_{{\rm nt}}/\dot{E}$ , where $\dot{E}$ is the spin-down energy loss rate. Although the luminosity limits for the XMM-Newton observations are ∼2 orders of magnitude poorer than for the Chandra observation of J1840−1419, the $\dot{E}$ values are correspondingly higher, such that for all three pulsars the limit turns out to be η ≲ 0.2. For their study of 39 pulsars, Possenti et al. (2002) determined that all sources had a value of η less than $\eta _{{\rm max}} = 10^{-18.5}(\dot{E}/\mathrm{erg}\,\mathrm{s}^{-1})^{0.48}$ . Our η limits are all significantly higher than this predicted value. However, we note that this critical η value is arrived at upon considering pulsars studied in the 2–10 keV energy range, narrower than the observations reported here.

These observations bring the total number of rotation-powered NSs with detections of thermal emission, or upper limits thereupon, to 49. In Figure 1 we show our limits, along with all previous measurements and limits. Zhu et al. (2011) suggest that there is a "hint" that the high magnetic field pulsars are hotter than the low magnetic field pulsars. To quantify this we first ignored the upper limits and divided the remaining data into "low" and "high" magnetic-field-strength sources, below and above an arbitrarily chosen field strength value of 10¹³ G. We also excluded three "low" magnetic-field-strength sources as their fitted blackbody radii are so much smaller than those of the rest of the sources (at 33, 43, and 120 m) so that their thermal emission is thought to be due to some heating process (Misanovic et al. 2008). Comparing the two distributions with a Kolmogorov–Smirnov (K-S) test, we find a K-S statistic of D = 0.33, and thus a probability of 0.31 that these two distributions are the same. There is therefore no evidence that the high magnetic field pulsars are hotter than those with lower magnetic fields. However, we note the caveat that, in addition to the age estimates being uncertain (as mentioned above), the magnetic field estimates are uncertain, and should only be considered accurate to within an order of magnitude. Knowledge of the inclination angles between the magnetic and rotation axes would be needed to estimate the magnetic field strengths more accurately (e.g., as in Spitkovsky 2006).

This work has been supported by NASA CXO guest observer support grant GO1-12059X, and made use of software provided by the Chandra X-ray Center. E.F.K. thanks the FSM for support, K. J. Lee for useful discussions on statistics, R. P. Eatough for useful comments on the manuscript, and the anonymous referee for providing valuable input that improved the quality of this paper. M.A.M. is supported by the Research Corporation for Scientific Advancement.

PSR J1840−1419: A VERY COOL NEUTRON STAR

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ABSTRACT

1. INTRODUCTION