X-Ray Measurement of the Spin-Down of Calvera: A Radio- And Gamma-Ray-Quiet Pulsar

Abstract

We measure spin-down of the 59 ms X-ray pulsar Calvera by comparing the XMM-Newton discovery data from 2009 with new Chandra timing observations taken in 2013. Its period derivative isṖ = (3.19 ± 0.08) × 10 −15 , which corresponds to spin-down luminosityĖ = 6.1 × 10 35 erg s −1 , characteristic age τ c ≡ P /2Ṗ = 2.9 × 10 5 yr, and surface dipole magnetic field strength B s = 4.4 × 10 11 G. These values rule out a mildly recycled pulsar, but Calvera could be an orphaned central compact object (anti-magnetar), with a magnetic field that was initially buried by supernova debris and is now reemerging and approaching normal strength. We also performed unsuccessful searches for high-energy γ -rays from Calvera in both imaging and timing of >100 MeV Fermi photons. Even though the distance to Calvera is uncertain by an order of magnitude, an upper limit of d < 2 kpc inferred from X-ray spectra implies a γ -ray luminosity limit of <3.3 × 10 32 erg s −1 , which is less than that of any pulsar of comparableĖ. Calvera shares some properties with PSR J1740+1000, a young radio pulsar that we show by virtue of its lack of proper motion was born outside of the Galactic disk. As an energetic, high-Galactic-latitude pulsar, Calvera is unique in being undetected in both radio and γ -rays to faint limits, which should place interesting constraints on models for particle acceleration and beam patterns in pulsar magnetospheres.

DEEP OPTICAL OBSERVATIONS OF UNUSUAL NEUTRON STAR CALVERA WITH THE GTC∗

“…Interestingly, the calculations given in Shibanov et al (1995) result in a similar dependence of the pulsed fraction on photon energy as observed for Calvera. Namely, Halpern et al (2013) found that the pulsed fraction is ≈ 10% at energies below 0.5 keV and ≈ 30% above 0.5 keV, which is in accord with the pulsed fraction calculated for the NS with dipole magnetic field B = 10 12 G covered by the hydrogen atmosphere .…”

Calvera: A Low-mass Strangeon Star Torqued by Debris Disk?

“…Assuming a magnetic field B = 10 12 G, they obtain good fits in spite of the viewing geometry. These results are broadly consistent in the sense that T ∞ ∼ 200 eV for blackbody models and T ∞ 100 eV for NSA models and emission area R ∞ /d = 2 − 4 km kpc −1 (Rutledge et al 2008;Shevchuk et al 2009;Zane et al 2011;Halpern et al 2013;Shibanov et al 2016). In our SSA model, we obtain a higher temperature at 0.6 keV and rather unconstrained radius R ∞ /d = 0.4 − 10 km kpc −1 .…”

“…As is shown in Shevchuk et al (2009), Zane et al (2011) and Halpern et al (2013), single thermal spectra, either blackbody or pure hydrogen atmospheric model (NSA), can not provide decent fit, and two thermal components is required. The first joint fit for all available data is performed by Shibanov et al (2016), who use a single component magnetized hydrogen atmosphere model to account for the inhomogeneities of the stellar surface.…”

“…It is odd that deep search failed to detect the radio emission from this source (Hessels et al 2007;Zane et al 2011). The non-detection of radio emission from Calvera can not be simply attributed to the unfavored beaming effect since emission features are nor found in gamma-rays (Halpern 2011;Halpern et al 2013) which commonly correspond to a larger beaming angle. This can be explained by a distant location of Calvera (e.g.,1.5 − 5 kpc, Shibanov et al 2016), but that would place it high above the Galactic disk and cause problem for its birth place, given its rather small proper motion (69 ± 26 mas yr −1 , Halpern & Gotthelf 2015).…”

Atmospheres and radiating surfaces of neutron stars

“…Calvera is also unique in that it is the only energetic pulsar that emits virtually no radio nor gamma radiation, which places constraints on models for particle acceleration in magnetospheres [170].…”