Spin clustering of accreting X-ray neutron stars as possible evidence of quark matter Page: 4 of 5
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FIGURE 5. Calculated spin distribution of the underlying population of x-ray neutron stars for one accretion rate (open his-
togram) is normalized to the number of observed objects (18) at the peak. Data on 18 neutron stars in LMXBs (shaded histogram)
is from Ref. [7]. The spike in the calculated distribution corresponds to the spinout of the quark matter phase. Otherwise the spike
would be absent.
FIGURE 6. Data on the frequency distribution of 60 millisecond pulsars (1 < P < 10 ms). The frequency bins are 50 Hz wide.
The theory and parameters used to describe our model neutron star are precisely those used in previous publications
[15]. Its initial mass is M = 1.42M, close to the mass limit of the rotating star of 1.66M. Quark matter is treated in
a version of the MIT bag model with the three light flavor quarks (m, = md = 0, ms = 150 MeV) as described in Ref.
[27]. A value of the bag constant BI/4 = 180 MeV is employed, as in [15]. The transition between these two phases of
a medium with two independent conserved charges (baryon and electric) is described in Ref. [13].
Figure 3 shows how the moment of inertia changes for a neutron star in a binary system that is spun up by mass
accretion according to Eq. (2). In one case we assume that a phase transition between quark matter and confined
hadronic matter occurs, and in the other that it does not. This accounts for the different initial moments of inertia, and
also, as we see, the response to spinup. Three average accretion rates are assumed, M_1o = 1, 10 and 100 (where M_10
is in units of 10-10M/y). The corresponding spin evolution of accreting neutron stars as determined by the changing
moment of inertia and the evolution equation (2) is shown in Fig. 4. In both Figs. 3 and 4 we assume that 0.4M is
accreted. Otherwise the maximum frequency attained is less.
We compute a frequency distribution of x-ray stars in low-mass binaries (LMXBs) from Fig. 4, for one accretion
rate, by assuming that neutron stars begin their accretion evolution at the average rate of one per million years. A
different rate will only shift some neutron stars from one bin to an adjacent one. The donor masses in the binaries are
believed to range between 0.1 and 0.4M and we assume a uniform distribution in this range. The resulting frequency
distribution of x-ray neutron stars is shown in Fig. 5; it is striking. Spinout of the quark matter core as the neutron
star spins up is signalled by a spike in the distribution which would be absent if there were no phase transition in our
model of the neutron star. The position of the spike depends only on the stellar model. But the weight of the spike as
compared to the high frequency tail depends sensitively on the weight with which the donor masses are assigned, the
initial mass function of the accreting neutron stars (for which we have taken only one mass), and to a minor degree
on the accretion rate. A donor of mass 0.1M contributes only to the spike, while all greater masses contribute to
the spike and to higher frequency x-ray stars. Objects above about 400 Hz are unstable to collapse to very high-spin
black holes. Accretors of lower initial mass than we assume would contribute to the long high-frequency tail as well,
possibly, to the spike.
DISCUSSION AND SUMMARY
Theoretically, a phase transition can (but not necessarily does) cause a distinct clustering in frequency of x-ray
accreters, which is independent of details of accretion, such as rate, mass accreted so long as it exceeds a small
minimum value (- 0.1M), or indeed to the particular description of accretion mechanism that we employ. As4
(dM/dt)_,=1
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Glendenning, Norman K. & Weber, Fridolin. Spin clustering of accreting X-ray neutron stars as possible evidence of quark matter, article, June 27, 2001; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc742886/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.