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PHY - LIGO, OPERATIONS & ADVANC R&D
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Gravitational Radiation from Accreting Neutron Star X-ray Sources:
Modeling and LIGO Data Analysis
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Page 2 of 2
Gravitational Radiation from Accreting Neutron Star X-ray Sources:
Modeling and LIGO Data Analysis
PROPOSAL SUMMARY
1) Intellectual merit: We propose to continue our studies of rapidly rotating neutron
stars in X-ray binaries as sources of persistent gravitational radiation detectable by
LIGO/VIRGO. Our parameterized evolution code, which follows the (r-mode)
perturbation amplitude, angular velocity, and temperature of the neutron star, will be
generalized to include recent theoretical and observational developments. One is the
gravitational wave spindown and r-mode heating of the neutron star that may be
observable during the “quiescent” phases of the transient class of these X-ray sources.
Another is the saturation of the amplitude at a small value, which can produce a
distinctively different type of evolution. We plan to work closely with X-ray observers to
improve our knowledge of those sources which are candidates for detectable gravitational
wave production. Further observations of the cooling of isolated neutron stars will also
improve our theoretical models of the neutrino luminosity. The major new focus will be
the development of robust algorithms for extracting the signal from the LIGO data. Such
a detection would give us unique information about various aspects of physics under
extreme conditions. Incorporating observational constraints on a) the spin period, b)
binary orbit parameters, and c) fluctuations in the gravitational wave frequency (from Xray flux monitoring) will be an important component of our effort to generalize the
existing codes for isolated periodic sources. Involvement of members of the Stanford
experimental LIGO group and Kavli Institute for Particle Astrophysics and Cosmology
(KIPAC) will be strong. Support for a postdoctoral researcher and a present KIPAC
Hubble Fellow as well as a graduate student is requested to help initiate this effort. Four
leading researchers at other institutions (in data analysis, X-ray observations, and
theoretical physics) have agreed to be collaborators. Of course, we plan to also work
closely with other members of the periodic source group of the LIGO Scientific
Collaboration. This proposal complements Stanford's ongoing experimental program on
advanced gravitational wave detectors, currently funded under NSF grant PHY-0140297,
for which a renewal proposal (NSF proposal number 0502641) has recently been
submitted.
2) Broader impact: This research supports the worldwide ground-based effort (LIGO,
GEO, VIRGO, TAMA, AURIGA, ...) to view and probe the universe in a fundamentally
different way. The public has demonstrated a strong interest in the nature of very strong
gravitational fields and the extreme physical conditions within neutron stars. Outreach
efforts will be coordinated with the Stanford experimental LIGO group, as detailed in
their parallel proposal. We will be aided in this effort by Stanford's Office of Science
Outreach.
TABLE OF CONTENTS
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Total No. of
Pages
Page No.*
(Optional)*
Cover Sheet for Proposal to the National Science Foundation
Project Summary
(not to exceed 1 page)
1
Table of Contents
1
Project Description (Including Results from Prior
NSF Support) (not to exceed 15 pages) (Exceed only if allowed by a
specific program announcement/solicitation or if approved in
advance by the appropriate NSF Assistant Director or designee)
13
References Cited
3
Biographical Sketches
(Not to exceed 2 pages each)
Budget
2
7
(Plus up to 3 pages of budget justification)
Current and Pending Support
1
Facilities, Equipment and Other Resources
1
Special Information/Supplementary Documentation
3
Appendix (List below. )
(Include only if allowed by a specific program announcement/
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Assistant Director or designee)
Appendix Items:
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Complete both columns only if the proposal is numbered consecutively.
PROJECT DESCRIPTION
1.
Background
The Laser Interferometer Gravitational Wave Observatory (LIGO) has begun its search for
gravitational waves from astrophysical sources (http://www.ligo.caltech.edu/). Because of its
broad-band response, its search and detection capabilities for persistent sources are especially powerful. Persistent sources can be defined to be those that produce potentially detectable gravitational
wave (GW) signals, typically at a single slowly varying frequency, for at least a few months. Because of the time dependence induced by the rotation and revolution of the earth, such a signal is
potentially easier to verify than that of burst or stochastic (background) radiation. We shall not
include inspiralling binaries or isolated radio pulsars in our investigations, since many other groups
are involved in their analysis. During the three-year duration of our proposed research, we plan
to continue our focus on the most promising of the remaining persistent sources: neutron stars
spun up to rapid rotation by accretion in low-mass X-ray binaries (LMXBs), and distorted by an
unstable r–mode (or possibly other mechanisms).
Since the launch of the Rossi X-ray Timing Explorer (RXTE) satellite, we have acquired significantly more relevant information about these LMXBs. There is now strong evidence (Chakrabarty
et al. 2003) that the oscillations detected during X-ray bursts in accreting LMXBs asymptotes to
the spin frequency of the neutron star, as separately measured in the coherent millisecond X-ray
pulsar LMXBs. The distribution of spin periods of these LMXBs, as well as those of radio pulsars,
indicates that gravitational radiation may be limiting the accretion–driven spinup of these neutron
stars (Bildsten 1998; Wagoner 1984; Chakrabarty et al. 2003).
The proposed Principal Investigator (Wagoner) is the member of the Stanford LIGO group
(Robert Byer, P.I.) presently involved in source modeling. He is also a member of the Astrophysical
Source Identification and Signatures (ASIS) working group of the LIGO Scientific Collaboration
(LSC). Stanford was initially identified by ASIS as a group to lead the effort to develop ‘Robust
Algorithms’ to search for continuous wave (CW) signals (LSC Data Analysis White Paper, 1999).
Such codes involve ‘specialized methods capable of searching for (such) waves from poorly modeled
sources’.
The P.I. plans to direct a significant portion of his research efforts into the areas indicated in this
proposal, helping to broaden the Stanford effort to include data analysis. In particular, we propose
to hire a postdoctoral research fellow and graduate student to help initiate this expansion of scope.
This will be carried out within the recently formed Kavli Institute for Particle Astrophysics and
Cosmology (KIPAC) at Stanford (Roger Blandford, Director and Steven Kahn, Deputy Director),
where there exists rapidly expanding expertise in various aspects of this research. KIPAC has
identified this area as one that they would like to support. A KIPAC Hubble Fellow (Wynn Ho)
will also participate in this research.
From 1991–2001, Wagoner concentrated to a large extent on relativistic diskoseismology (normal modes of oscillation of accretion disks around black holes and neutron stars), e. g., Wagoner
(1999). Earlier, some of his contributions to the field of gravitational radiation were:
a) Calculation of the gravitational radiation damping of the orbit of the Hulse-Taylor binary pulsar (Wagoner 1975) and from general binary systems through post-Newtonian order (Epstein &
Wagoner 1975; Wagoner & Will 1976).
b) Calculation of the gravitational wave flux (proportional to the X-ray flux) from steadily accreting
neutron stars (Wagoner 1984).
c) Analysis of multi-mode detection of gravitational waves by spherical resonant-mass detectors
(Wagoner & Paik 1977; Wagoner 1997).
d) Gravitational wave observations as a tool for testing relativistic gravity (Eardley, Lee, Lightman,
Wagoner & Will 1973).
e) Production and detection of scalar gravitational waves (Wagoner 1970; Wagoner & Kalligas
1997).
The proposed Co-Investigators (Lantz and Robertson) have been leaders in the Stanford experimental LIGO group. They will help to implement and coordinate this proposed expansion to
data analysis. In particular, their understanding of the experimental techniques used in the LIGO
detectors will add an important perspective to the interpretation of the data. Brian Lantz serves as
the lead on science questions relating to the hydraulic external pre-isolator (HEPI) installation at
the LIGO Livingston Laboratory (LLO). He has made several trips to LLO to work on the initial
installation and commissioning of HEPI, and consults regularly on its operation. He also has extensive experience of interferometry, having worked on the phase noise interferometer at MIT. Norna
Robertson has been active in the field of gravitational wave detection for more than 20 years, most
recently in the areas of suspension and vibration isolation. Previously she has worked on thermal
noise and optical aspects of detection. She currently holds the position of cognizant scientist for
suspensions in Advanced LIGO. Both have already gained experience as science monitors during
science runs and propose to continue this role, funded on the complementary Stanford experimental
program (NSF proposal 0502641). In this proposal we are requesting funding for further LIGO site
visits to allow Lantz and Robertson to gain a deeper understanding of the operation and behavior
of the detectors.
2.
Recent Relevant Research by Our Group
From September 2000 – September 2003, Wagoner’s theoretical research in this area was supported by NSF grant PHY-0070935, ‘Persistent Gravitational Radiation: Sources and LIGO Detection’. (The total funding was $ 85,025 over the three-year period, which restricted the effort
involved.) Here we summarize the results of that research, much of which can be found in three pa2
pers by Wagoner, Hennawi & Liu (2001) and Wagoner (2002, 2004). At the beginning of the grant
period, Wagoner and a Stanford M.S. student (Joe Hennawi) and Ph.D. student (Jingsong Liu)
completed our initial investigation of the evolution of rapidly rotating accreting neutron stars under the influence of their emission of gravitational radiation. This work was presented at the 20th
Texas Symposium on Relativistic Astrophysics (Wagoner, Hennawi & Liu 2001). An additional
commentary on some very relevant X-ray observations appeared in Nature (Wagoner 2003).
We have developed a modified and extended two-component model of the star (axisymmetric
equilibrium plus perturbation) introduced by Owen et al. (1998) and also employed by Levin
(1999). It is certainly valid in our case, since we shall need to consider only small perturbations.
The perturbation is taken to be produced by an r–mode (Andersson 1998; Friedman & Morsink
1998; Lindblom, Owen & Morsink 1998; Andersson, Kokkotas & Schutz 1999), rather than by
temperature-induced inhomogeneous electron-capture layers (Bildsten 1998). The r–modes are
more powerful emitters of gravitational radiation than the f–modes studied by Chandrasekhar
(1970) and Friedman & Schutz (1978). The dominant (l = m = 2) r–mode (velocity perturbations
δv driven by the Coriolis force) is characterized by an amplitude α ∼ δv(r = R)/ΩR, where
Ω = 2π/P and R are the angular velocity and radius of the neutron star. We follow the evolution
of the (uniform) angular velocity Ω(t) and average core temperature T (t) of the neutron star,
in addition to the amplitude α(t). With J∗ (M, Ω) the angular momentum of the equilibrium
axisymmetric neutron star, its total angular momentum is J = J∗ +(1−Kj )Jc , where the canonical
angular momentum is Jc = −Kc α2 J∗ . (These constants K( ) ≈ 0.1 − 1.)
2.1.
Governing relations
The evolution is governed by the following equations. The angular momentum perturbation
obeys the relation
dJc /dt = 2Jc [(Fg (M, Ω) − Fv (M, Ω, T )] .
(1)
−1 (Ω/Ω )6 , with τ ∼ 3 seconds for the neutron
The gravitational radiation growth rate is Fg = τgr
c
gr
star model adopted (Owen et al. 1998) and Ωc ≡ (πGhρi)1/2 . In what follows, we shall neglect the
dependence on the slowly increasing mass M .
The viscous damping rate is
Fv ∼
= Fbl (Sn , Ss , B; Ω, T ) + Fhb (Th ; Ω, T ) ,
where B is the magnetic field strength in the core–crust boundary layer and Th is the hyperon
superfluid transition temperature. We have modified the viscous and magnetic boundary layer
damping rate (Fbl ) of Kinney and Mendell (2003), with the slippage factors (Levin & Ushomirsky
2001) S for the normal and superfluid components. The contribution of ordinary core shear viscosity
is much less. The hyperon bulk viscosity damping rate (Fhb ) due to n + n n + Λ, p + Σ− , etc.
employs results of Lindblom & Owen (2002) and Haensel, Levenfish, and Yakovlev (2002). (But
3
very recently van Dalen & Dieperink (2004) obtained a smaller rate.) The contribution to this
damping rate from the mutual friction between a neutron superfluid and the superconducting
proton–relativistic electron fluid (Lindblom & Mendell 2000) is negligible. We have also neglected
damping via energy extraction from the mode to magnetic fields (Rezzolla, Lamb & Shapiro 2000;
Rezzolla et al. 2001), since it requires larger magnetic fields (B & 1011 Gauss) than should exist
within LMXBs.
Conservation of total angular momentum requires that
dJ/dt = 2Jc Fg + ja M˙ (t) − TB (M˙ ) .
(2)
The first (negative) term is due to gravitational radiation, the second to accretion [at the rate
M˙ (t)], and the third is the magnetic torque of the disk on the star [e.g., Rappaport, Fregeau &
Spruit (2003)].
From these relations, we can obtain the spin evolution equation
I∗ dΩ
TB
(ja − j∗ ) ˙
M (t) −
,
= −2[Kj Fg + (1 − Kj )Fv ]Kc α2 +
J∗ dt
J∗
J∗
and the amplitude evolution equation
1 dα
= Fg − Fv + [Kj Fg + (1 − Kj )Fv ]Kc α2 −
α dt
ja
2J∗
TB
M˙ (t) +
,
2J∗
(3)
(4)
where I∗ (M, Ω) = ∂J∗ /∂Ω ≈ J∗ /Ω and j∗ (M, Ω) = ∂J∗ /∂M ∼ J∗ /M .
Finally, thermal energy conservation for the star gives
Z
∂T
dT ∼ ˜
cv dV ≡ C(T )
= 2Ec Fv (Ω, T ) + Kn hM˙ in c2 − Lν (T ) ,
∂t
dt
(5)
˜c =
where the r–mode viscous heating is proportional to the rotating frame canonical energy E
2
(Kc /3)J∗ Ωα . The inner crust nuclear heating is driven by an accretion rate hM˙ in , averaged over
the nuclear time scale τn ∼ 1 year (Wijnands et al. 2002). The constant Kn ≈ 1 × 10−3 . The
neutrino luminosity Lν (which dominates that of the surface photons) includes contributions from
the direct Urca reactions, modified Urca reactions, (inner crust) electron–ion and (core) neutron–
neutron neutrino bremsstrahlung, and Cooper pairing of (inner crust) neutrons. The expressions
for these contributions, including the superfluid suppression factors for the direct and modified Urca
reactions, were obtained from the review of Yakovlev, Levenfish & Shibanov (1999). Comparison of
observations of thermal emission from isolated neutron stars with computed cooling histories has
led Kaminker, Yakovlev, and Gnedin (2002) to propose that at the core temperatures of interest
here (T ∼ 3 × 108 K) the core (triplet) neutrons are normal, while the core (singlet) protons and
inner crust (singlet) neutrons are superfluid. We adopted these assumptions.
√
For typical values of Ω, T , and hM˙ i < M˙ Edd ∼ 3 × 10−8 M /yr (with ja ∼ GM R), we obtain
three key time scales (gravitational radiation, cooling, and accretion):
τg ≡
1
∼ 103 sec ,
Fg
τc ≡
C(T )T
∼ 103 yr ,
Lν (T )
4
τa ≡
J∗
& 107 yr .
ja hM˙ ia
These time scales are seen to be relaxation times of our evolution equations (1), (5), and (3),
respectively. Here the accretion rate is averaged over the time scale τa .
2.2.
Evolution
We have followed the evolution of neutron stars after they have been spun up to the point
where equation (1) vanishes: Fg (Ωin ) = Fv (Ωin , Tin ). This equality defines our initial state, where
the perturbation can begin to grow. The initial temperature Tin is determined by the vanishing of
equation (5), with the nuclear heating balanced by the neutrino emission.
In contrast to the initial state, the equilibrium state is defined by the vanishing of the evolution
equation (3), in addition to the evolution equations (1) [or(4)] and (5). The equilibrium amplitude
is then given by αeq = [τg /(2Kc τa )]1/2 ∼ (10−7 − 10−5 ), assuming that the magnetic torque is
negligible.
In Fig. 1 we show the ‘critical curve’ defined by Fg (Ω) = Fv (Ω, T ), for a somewhat optimistic
choice of damping rate parameters. On it are indicated the initial and equilibrium states for
two choices of (time averaged) mass accretion rate. The linear perturbation analysis of Wagoner,
Hennawi & Liu (2001) shows that stability of the equilibrium state requires that the slope dΩ/dT >
0.
We have shown how the evolution from the initial state is also controlled by the sign of the
slope dΩ/dT of the critical curve:
• If the slope is negative [as in Fig. 1, case (a)], there will be a thermal runaway (dT /dt > 0,
1/2
dΩ/dt ≈ 0) with a growth rate Kr αeq /τg ∼ 1/yr that is of the same magnitude as found by Levin
(1999). Here Kr ∼ 105 is the ratio of rotational to thermal energy in the star. This will end when
either (a) the amplitude saturates [at a value α . 10−3 (Arras et al. 2003)] and the neutron star
then spins down to the critical curve with α ≈ constant (Heyl 2002; Arras et al. 2003), or (b) the
neutron star reaches the stable portion of the critical curve before the amplitude saturates.
• If the slope is close to zero, there will initially be overstable oscillations of the type found by
Wagoner, Hennawi & Liu (2001).
• If the slope is positive [as in Fig. 1, case (b)], the oscillations of the growing amplitude are damped
out on a timescale ∼ τc , after which it slowly increases toward its equilibrium value, as shown in
Fig. 2. The evolution of Ω and T is similar, with the time required to reach the equilibrium state
given by
∆t ≈ [(Ωeq − Ωin )/Ω]τa .
If the magnetic torque term in equation (3) were important, τa could be appropriately modified.
After accretion ceases, the star spins down along the critical curve.
5
-7
0.45
-8
Log10 Amplitude
WWc
0.5
0.4
0.35
-9
-10
-11
0.3
1
2
3
4
5
-12
6
1
T108 K
3
Log10 Htt* L
2
4
5
Fig. 1.— The relation between dimensionless angular velocity Ω/Ωc (≈ 2/3 at the shedding limit)
and temperature T8 on the critical curve Fg (Ω) = Fv (Ω, T ). The model chosen has a normal
fluid hyperon damping rate 10 times greater than that of Lindblom & Owen (2002), a hyperon
superfluid transition temperature Th = 1 × 109 K, core–crust slippage factors Sn = Ss = 0.2, and
boundary-layer magnetic field B . 109 G. Also shown are the initial and equilibrium states for
(a) hM˙ ia = M˙ Edd /300: T8 (in) = 1.84, T8 (eq) = 2.44 and for (b) hM˙ ia = M˙ Edd /3: T8 (in) = 3.32,
T8 (eq) = 3.73.
Fig. 2.— The early evolution of the r-mode amplitude α, for M˙ = M˙ Edd /3. The initial amplitude
(during spinup to the critical curve) was chosen to be α0 = 10−12 , and t∗ = 1 yr. When equilibrium
is reached, αeq = 3.60 × 10−6 .
The ratio of the spindown rate to spinup rate along the critical was shown to be
P −1 dP/dt(M˙ hM˙ ia )
Ω 6 α 2
.
≈−
Ωeq
αeq
P −1 dP/dt(M˙ = hM˙ ia )
(6)
We also found that on the critical curve, the ratio of r–mode heating to accretion–induced nuclear
heating in equation (5) is
˜ c Fg
2E
hM˙ in (eq)
≈ 10
Kn hM˙ in c2
hM˙ in
Ω
Ωeq
8 α
αeq
2
.
(7)
If the neutron star reaches a positive slope section of the critical curve in any way, equations (1)
and (5) quickly relax to equilibrium. So further evolution occurs at a rate governed by equation (3)
(whose first term is now −2Kc Fg α2 ), with steady gravitational radiation generated by the r–mode
amplitude given by the vanishing of equation (5) (with Fg = Fv ):
α2 = (Lν − Kn hM˙ in c2 )/[(2Kc /3)J∗ ΩFg ] .
(8)
This remains true as long as dΩ/dT > 0. After accretion ceases, the star will spin down until this
slope vanishes (Reisenegger & Bonaˇci´c 2003). Then the star will cool further at constant Ω, no
6
longer emitting gravitational waves (α negligible). It then can become a millisecond radio pulsar
(Reisenegger & Bonaˇci´c 2003).
After T increases slightly above Tin , the neutrino luminosity dominates the nuclear heating
(for constant hM˙ in ) in equation (8). In Fig. 3 is plotted the resulting amplitude at any point on the
positive slope section of the critical curve. Using this amplitude, we show in Fig. 4 the spindown
rate when the accretion and magnetic torques are smaller than that due to gravitational radiation
in equation (3).
Log10 @P-1 dPdt Hyr-1 LD
r-mode amplitude
0.000016
0.000014
0.000012
0.00001
-6
8·10
-6
6·10
-6
4·10
-6
2·10
2.75
3
3.25 3.5 3.75
T108 K
4
-6
-6.5
-7
-7.5
-8
-8.5
-9
4.25 4.5
2.75
3
3.25 3.5 3.75
T108 K
4
4.25 4.5
Fig. 3.— The r–mode amplitude α at any point on the stable section of the critical curve where
Lν Kn hM˙ in c2 .
Fig. 4.— The spindown rate produced by gravitational radiation when the neutron star is on the
stable section of the critical curve.
Observations of transient LMXBs during their quiescent states (when M˙ (t) hM˙ i) provide
the opportunity to detect two signatures that the neutron star is emitting gravitational radiation
at the rate predicted if it has evolved to the stable portion of the critical curve. We found that in
order that such a positive slope portion exist, the neutron star core must contain hyperons with a
moderate superfluid transition temperature (∼ 109 K) and neutrons with a low superfluid transition
temperature (∼ 108 K).
The first signature was pointed out by Brown & Ushomirsky (2000), who showed that observations of the X-ray luminosity during quiescence (when the emission from the surface can be greater
than that from the accretion disk and its ‘corona’) can place interesting limits on the amount of
r–mode heating. We have also estimated the photon luminosity, and obtained results similar to
theirs for a ‘normal core’. They assumed that the star was in the equilibrium state. Note however
that during spinup to or spindown from this state, the mode heating (∝ Ω8 α2 ) will be less than they
employed. Within the uncertainties of the neutrino luminosities consistent with observations of isolated neutron stars (Yakovlev & Pethick 2004; Yakovlev et al. 2004), comparison with observations
of the four quiescent sources with large spin frequencies allows the presence of the predicted level
of r–mode heating. However, this extra source of heating is certainly not yet required (Yakovlev et
7
al. 2004).
We have focused on the second signature. When the accretion torque becomes negligible at
sufficiently small values of M˙ (t), the constant gravitational wave torque provides a fixed lower limit
to the spindown rate, shown in Fig. 4. If the contribution of magnetic torque can be identified from
its dependence on M˙ (t) and removed, a constant residual will provide evidence that the neutron
star is emitting gravitational radiation at a significant rate. The transient XTE J0929-314 was
observed to have an average spindown rate P −1 dP/dt ≈ 1.6 × 10−8 per year (Galloway et al. 2002),
comparable to that in Fig. 4 for a core temperature T ≈ 3.5 × 108 K. The transient SAX J1808.43658 was observed to spin down at about the same rate after an outburst in 2002, but spun up by
a larger amount during its 1998 outburst (Morgan, Galloway & Chakrabarty 2003). As more data
accumulate, it should be possible to extract more information about the contributions to spindown
in the candidate (high spin frequency) neutron star transients.
If the magnetic torque is negligible in equation (2), in any equilibrium state (independent of
the nature of the neutron star distortion) the gravitational-wave (GW) flux is proportional to the
average X-ray flux (proportional to hM˙ ia ), which produces a metric perturbation (strain) amplitude
(Wagoner 1984)
1/2 −1/2
Fγ
fgw
−27
h ≈ 4 × 10
,
(9)
10−8 erg cm−2 s−1
600 Hz
where Fγ is the detected (X-ray) energy flux and fgw is the frequency of the gravitational wave.
For the dominant r–mode, the gravitational wave frequency is fgw = 4/(3P ) = 2Ω/(3π), plus
corrections of O(GM/Rc2 ) and O(Ω/Ωc )2 (Yoshida, Yoshida & Eriguchi 2004). If the neutron star
is not in the equilibrium state but is on the stable portion of the critical curve, the GW strain
scales as h ∝ Ω3 α.
In summary, our major contributions during this three-year period were
a) Correcting and including external torques and all the possibly relevant processes of neutrino
cooling in the basic equations of evolution.
b) Showing the various types of gravitational wave evolution that are possible on or near the critical
curve.
c) Demonstrating the potential importance of hyperon bulk viscosity in allowing persistent emission
of gravitational radiation from LMXBs. In particular, we showed (Wagoner 2002) that a stable
portion of the critical curve exists if (a) a significant fraction of the core of the neutron star is above
the threshold for producing hyperons (which requires high mass), (b) their superfluid transition
temperature Th . 2×109 K, (c) the core neutrons near the crust are not a superfluid whose vortices
are strongly pinned to the crust, and (d) the magnetic field is not too strong (B . 1010 G) in that
core–crust boundary layer.
d) Pointing out that spindown due to gravitational radiation may be detectable in quiescent LMXBs
(Wagoner 2004).
8
3.
Proposed Research
As indicated above, we propose to evolve our LIGO-related research from modeling the evolution of this class of accreting neutron stars to a development of algorithms for extracting the
predicted GW signal from the noise. One of our goals is the development of a parameterized expression describing the time evolution of the GW phase and amplitude. We describe these two
components below, anticipating an emphasis on the latter.
3.1.
Modeling the gravitational radiation evolution of accreting neutron stars
We plan to improve our evolution code (outlined above) in various ways, which we will describe
below. Our goal is to identify the possible types of evolution of LMXBs which are candidates for
either direct GW detection, or indirect detection via the properties (discussed above) of transient
LMXBs in their ‘quiescent’ phase.
We will continue to update the damping rate (Fv ), which most importantly determines the
critical curve. For instance, when the core–crust boundary layer dominates the viscous damping
(which occurs at least at the lower core temperatures), Ω ∝ T −2/11 on the critical curve (if the
magnetic effects are negligible, as anticipated). We plan to investigate a key uncertainty, the rigidity
of the (inner) crust (Levin & Ushomirsky 2001). The contribution of the hyperon bulk viscosity
to the damping rate depends most sensitively (roughly exponentially) on the superfluid transition
temperature (Tc ) of the hyperons, which is poorly constrained. If it is not much higher than the
core temperature, it produces the stable section of the critical curve at the higher core temperatures
(see Fig. 1). The abundance of hyperons depends upon the mass as well as the equation of state of
the star. One of our proposed collaborators, Ben Owen, has discovered serious errors in previous
determinations of the hyperon bulk viscosity and is completing a new calculation.
A critical issue is the relation of the r–mode gravitational wave frequency (fgw ) to the spin
frequency (f ) of the neutron star, mentioned previously. Better estimates of the corrections to the
Newtonian value fgw /f = 4/3 will reduce the LIGO search space for fgw , assuming that X-ray
observations have provided a value of f that is less uncertain. Indications are that rapid rotation
tends to reduce this ratio, while strong gravitational fields tend to increase it (Yoshida, Yoshida
& Eriguchi 2004). The amounts may be up to ∼ 20%. Ben Owen is also very interested in this
problem, and we plan to begin collaborating on an improved calculation. The major problem is
the change of character of the governing equations when the Cowling approximation (neglect of
perturbations in the gravitational field) is dropped within a fully general relativistic approach.
We will also continue to update the neutrino emission rates, which also depend upon the mass
and equation of state of the neutron star. An important part of this effort is the incorporation of the
comparison of theoretical and observational (mostly X-ray) results for the neutrino cooling phase
of isolated neutron stars (Kaminker, Yakovlev, and Gnedin 2002; Tsuruta et al. 2002; Yakovlev &
9
Pethick 2004).
Our present code is based upon the assumption that the thermal conductivity timescales
(∼ 0.1 − 1 year) in the core are short enough to allow the use of a single spatially-averaged core
temperature. However, its radial dependence will become especially important when we consider the
surface emission during the ‘quiescent’ phases of transient LMXBs (Brown, Bildsten & Rutledge
1998; Colpi et al. 2001). The thermal conductivity timescales are less constrained in the crust
(Brown 2000). Calculation of the contribution of r–mode heating to this emission also requires
better knowledge of the neutrino emission rates mentioned above. Brown & Ushomirsky (2000)
assumed that the neutron star was in the equilibrium state, whereas we will only assume that it is
on the stable portion of the critical curve, or evolving with a constant r–mode amplitude αmax (see
below). We plan to include a radial dependence T (r, t) in the code. A key question is the thermal
timescale at the surface relative to the recurrence timescale of the bright X-ray phases.
It is also important, especially for the transient systems, to better model the torque due to the
magnetic coupling of the accretion disk to the neutron star. KIPAC Hubble Fellow Wynn Ho has
investigated various issues involving magnetic fields and neutron stars, and is planning to work on
this problem. A related problem is the value of the specific angular momentum (ja ) accreted from
the disk. Another need is a fuller investigation of the effect of magnetic fields on the crust–core
boundary layer viscosity.
In an important paper, Arras et al. (2003) obtained an r–mode amplitude saturation limit
αmax . 10−3 , produced by nonlinear coupling to inertial modes. If α increases to this value
during a thermal runaway, it will thereafter remain approximately constant until GW spindown
and associated cooling bring the system to the stable or unstable portion of the critical curve. This
−2 ) (Heyl 2002; Arras et al. 2003). If all the energy is lost as heat
can take an appreciable time (∝ αmax
at much smaller scales in the turbulent cascade, the r–mode heating term in our basic evolution
˜c Fg . We plan to incorporate (and further investigate) these aspects of
equation (5) becomes 2E
saturation in our evolution code. For instance, on what timescales and by how much can αmax
vary?
3.2.
Developing LIGO search algorithms
The main goal of this project is the development of algorithms to search for such GW signals
from candidate LMXBs, involving a parameterized expression for the time development of the
GW phase and amplitude. At least initially, we plan to build upon the approach developed by
Brady & Creighton (2000). It involves stacking of power spectra obtained from Fourier analysis of
successive demodulated (with the parameterized model) time series (of length ∆t). A hierarchical
strategy is also employed in which candidate signals (obtained with a lower threshold) are used as
the targets in a longer follow-up search in the neighborhoods of the particular sets of parameters
which characterize the candidates. In addition, the GW strain sensitivity of any such search could
10
be enhanced by a factor of order 10 if the interferometer were operated in a signal-recycled, narrowband mode (as is proposed for Advanced LIGO). We plan to consult with Patrick Brady, a leader
within the LSC who has agreed to be listed as one of our collaborators.
Since the search will be targeted on known LMXBs, the corrections for the Doppler effects of
the motion of the GW detector will be known. However, the effects of the motion of the neutron star
about its companion must be modeled with the orbital parameters, constrained from (optical and
infrared) observations of its companion and possibly its accretion disk, as well as X-ray observations
of the neutron star spin frequency. The formalism presented above will be used to model the phase
and amplitude of the waves in the frame of the neutron star. The development of algorithms for
this type of search is presently being carried out by a group headed by Alberto Vecchio, who is a
leader in the LIGO, VIRGO, and GEO efforts. He is anxious to have us join him in this effort, and
has agreed to be designated a collaborator.
The GW phase depends mainly on Ω(t), with the search near GW frequencies 4/3 and twice
as large (allowing for the corrections which we hope to make less uncertain, as indicated in Section
3.1). We note that if a large accretion rate (time scale τa ∼ 108 years) changes significantly during
∼ 3 days, the GW phase will differ by one cycle at the end of that period (Brady & Creighton
2000). This could be the limit to the coherent search interval ∆t. At least in principle, however,
monitoring the X-ray luminosity can provide information about the mass accretion rate. We will
investigate whether this can be useful in practice. The higher energy X-rays will presumably more
closely track what we want, the mass accretion rate at the surface of the neutron star.
The GW amplitude, which does not have to be known that accurately, depends (slowly) on α(t)
and Ω(t). We plan to parameterize the uncertain properties of the neutron star interior (indicated
above) which affect the evolution of α, Ω, and T . Note from above that except for this fluctuation
induced by the short-term variations of M˙ (t), the evolution of these three relevant properties of
the neutron star occur on either the accretion timescale τa or the (similar) GW spindown timescale
τg /α2 .
There are now at least twelve neutron stars in LMXBs whose angular velocities have been
firmly established by oscillations observed (by RXTE) during type I X-ray bursts and/or during
persistent X-ray emission (Chakrabarty et al. 2003; van der Klis 2000), whose spin frequencies lie
in the range 270 Hz ≤ f ≤ 619 Hz. We note that almost all models of neutron stars give a break-up
frequency at least twice as great as this upper limit (Cook, Shapiro & Teukolsky 1994). Many
[especially Bildsten (1998)] have argued that the torque due to the loss of angular momentum via
gravitational radiation could be limiting the spin frequency. These neutron stars presumably have
magnetic fields B . 108 gauss, weak enough to allow the accretion disk to extend close to the star
and thus deposit a large angular momentum per unit mass (ja ). In addition, there are now four
radio pulsars with spin frequencies near (above and below) the X-ray upper limit (Ransom 2004).
Another goal of this project is to better understand the presumed evolutionary relation between
the X-ray and radio spin frequencies.
11
From his work on diskoseismology, the P.I. is familiar with the techniques used by the RXTE
satellite team in their very successful search for quasi-periodic oscillations in the X-ray output from
neutron star and black hole LMXBs. We plan to keep abreast of developments in this area (hopefully
with similar capabilities on future satellites), with critical help from our proposed collaborator
Deepto Chakrabarty, in a search for more information about promising candidates for direct and
indirect GW detection. One very important aspect is the search for a steady component of spindown
(dP/dt) in the transient sources as a potential signature of GW emission. Another is a potential
correlation between high spin rates and excess ‘quiescent’ X-ray flux, if produced by the r–mode.
If Sco X-1 has been spun up by accretion to a stable equilibrium state, it should be detectable
by Advanced LIGO. We will strongly encourage a deeper search for its spin period. When signal
recycling (narrow-banding) is employed, a few additional LMXB’s may also be detectable (Bildsten
2003; Cutler & Thorne 2002). The candidates could contain some transient X-ray sources with high
spin rates, as well as the bright steady emitters (like Sco X-1). A major uncertainty is the actual
value of the (very) long–term average hM˙ ia (which controls the neutron star spinup), as inferred
from monitoring the X-ray flux (presently mostly with the ASM on RXTE). We propose to update
and extend the list of candidate LMXBs, allowing for states other than equilibrium and providing
revised estimates of the gravitational wave metric perturbation.
Although the accreting neutron star r–mode sources will be our initial focus, we will be prepared
to investigate other promising persistent sources that may emerge.
4.
Management, Interactions, Human Resources Development, and Outreach
The Principal Investigator plans to devote approximately half of his research time to this
project. He will be Emeritus, with 4.5 months of annual salary from Stanford from 1/2005 through
12/2007. Significantly reduced teaching duties will allow for greater concentration on this research.
The Co-Investigators are leading members of the Stanford experimental LIGO group. The main role
of the postdoctoral researcher to be hired is the development and testing of the search algorithm,
in collaboration with the P.I. and Co-I.s. KIPAC postdoctoral researcher Wynn Ho will continue
to be supported by his Hubble Fellowship during the first year of the proposed grant, and is to be
supported half time thereafter since he will devote that fraction to this project. Like the P.I., he
will investigate both theoretical and data analysis issues. Support is also requested for one graduate
student, for the data analysis development component.
This research will be strongly leveraged by the members and resources of KIPAC. Among
KIPAC physics faculty, we will benefit from ongoing discussions with Roger Blandford and Roger
Romani of relevant issues in neutron star physics and observation. There is also an overlap with
the numerical simulations of KIPAC Chandra Fellow Anatoly Spitkovsky on neutron star surfaces
and environments. In addition, we anticipate a continuation of useful input from some of the many
KIPAC visitors. The recently endowed Pierre Schwob computing and numerical simulation center,
12
to be a significant component of the main KIPAC building (at SLAC), will be developed by our
new KIPAC (Physics–SLAC) Associate Professor, Tom Abel (a leader in numerical simulations of
the development of the first stars, black holes, and galaxies in the universe). This resource will
greatly aid our efforts to develop and test the GW search algorithms. Five additional joint faculty
appointments will be made within KIPAC during the next few years.
Strong interactions with the wider community will be fostered by the agreement of four leading
researchers to collaborate within the key interfaces of this project, as indicated above. They
are (1) Data analysis: Patrick Brady (University of Wisconsin, Milwaukee) and Alberto Vecchio
(University of Birmingham), (2) Observational X-ray astronomy: Deepto Chakrabarty (M.I.T.),
and (3) Theoretical physics and astrophysics: Ben Owen (Penn State). Letters of commitment
are included in this proposal. We will be participating strongly in the presumed expansion of the
periodic source group of the LIGO Scientific Collaboration to include this class of GW sources.
Stanford University provides significant support for undergraduate research. The P.I. has had
a number of physics majors working on various research projects in gravitation and astrophysics
over the past few years, with some completing honors theses. In particular Joe Hennawi contributed
significantly to our earlier research on the topic of this proposal, as indicated above. Undergraduates
are supported fully by Stanford during the summer. We anticipate the involvement of one or two
such undergraduates in this proposed research.
This research supports the ground-based worldwide effort (LIGO, GEO, VIRGO, TAMA,
AURIGA, ...) to view and probe the universe in a fundamentally different way. The public has
demonstrated a strong interest in the nature of very strong gravitational fields and the extreme
physical conditions within neutron stars. Outreach efforts will be coordinated with the Stanford
experimental LIGO group, as detailed in their parallel proposal. We will be aided in this effort by
Stanford’s Office of Science Outreach.
13
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3
BIOGRAPHICAL SKETCH – Robert V. Wagoner
Present Position: Professor of Physics, Stanford University, 1977–present.
Previous Positions:
George Ellery Hale Distinguished Visiting Professor, University of Chicago; autumn quarter, 1978.
Sherman Fairchild Distinguished Scholar, California Institute of Technology; winter quarter, 1976.
Associate Professor of Physics, Stanford University; 1973–1977.
Assistant (1968–1971) and Associate (1971–1973) Professor of Astronomy, Cornell University; .
Visiting Fellow, Institute of Theoretical Astronomy, Cambridge University; 1967 and 1971.
Research Fellow in Physics, California Institute of Technology; 1965–1968.
Education:
B.M.E. (Mechanical Engineering), Cornell University; 1961.
M.S. (Engineering Science), Stanford University; 1962.
Ph.D. (Physics; Advisor: Leonard I. Schiff), Stanford University; 1965.
Research Interests: Theoretical astrophysics, cosmology, and gravitation.
Organizations: American Physical Society (Fellow), American Astronomical Society (High Energy
Astrophysics Division), International Astronomical Union, LIGO Scientific Collaboration.
Academic Awards:
John Simon Guggenheim Memorial Fellowship; 1979–1980.
Alfred P. Sloan Foundation Research Fellowship; 1969–1971.
Fifth Award for Essays on Gravitation; 1975.
Tau Beta Pi, Phi Kappa Phi honorary societies.
Recent National and International Committees:
Organizing Committee of the 22nd Texas Symposium on Relativistic Astrophysics, Stanford University;
December 13–17, 2004.
Program Advisory Committee of the National Science Foundation Center for Particle Astrophysics,
Berkeley; 1990–1998.
NASA RXTE Proposal Selection Committee, August 1996, 1997.
Visiting Committee, Canadian Institute of Theoretical Astrophysics, University of Toronto; November,
1994.
Grant Selection Committee for Space and Astronomy, Natural Sciences and Engineering Research Council of Canada; 1990–1993.
Five Relevant Publications
‘Test for the Existence of Gravitational Radiation’, Astrophysical Journal (Letters) 196, L63 (1975).
‘Post-Newtonian Gravitational Radiation from Orbiting Point Masses’ (with Clifford Will) Astrophysical
Journal 210, 764 (1976).
‘Gravitational Radiation from Accreting Neutron Stars’, Astrophysical Journal 278, 345 (1984).
‘Conditions for Steady Gravitational Radiation from Accreting Neutron Stars’, Astrophysical Journal
(Letters) 578, L63 (2002).
‘A Timing Signature of Gravitational Radiation from LMXB Neutron Stars’, in X-Ray Timing 2003:
Rossi and Beyond, edited by P. Kaaret, F.K. Lamb & J.H. Swank (AIP Conference Proceedings 714; Melville,
New York), p. 224 (2004).
Five Other Significant Publications
‘Big Bang Nucleosynthesis Revisited’, Astrophysical Journal 179, 343 (1973).
‘Aligned Rotating Magnetospheres.I. General Analysis’ (with E.T. Scharlemann), Astrophysical Journal
182, 951 (1973).
‘Determining q0 from Supernovae’, Astrophysical Journal (Letters) 214, L5 (1977).
‘Determining the Properties of Accretion-Gap Neutron Stars’ (with W. Kluzniak and P. Michelson),
Astrophysical Journal 358, 538 (1990).
‘”Stable” Quasi-Periodic Oscillations and Black Hole Properties from Diskoseismology’ (with Alexander
S. Silbergleit and Manuel Ortega-Rodriguez), Astrophysical Journal (Letters), 559, L25 (2001).
Collaborators Within Last 4 Years
Michael Nowak (M.I.T. Chandra Center), Jingsong Liu (Stanford University), Joseph Hennawi (Princeton University), Alexander Silbergleit (GP-B, Stanford), Manuel Ortega-Rodriguez (University of Costa
Rica), Dana E. Lehr (National Science Foundation), and J¨orn Wilms (Univeristy of Tubingen) .
Advisees Within Last 5 Years
Ph. D. thesis: Dana E. Lehr, David I. Santiago, Manuel Ortega-Rodriguez, and Jingsong Liu (all at
Stanford). (Total of 28 Ph. D. students.)
Advisors of P.I.
Graduate thesis: Leonard I. Schiff, Stanford University. Postgraduate: William A. Fowler, Caltech.
2
SUMMARY
YEAR 1
PROPOSAL BUDGET
FOR NSF USE ONLY
PROPOSAL NO.
DURATION (months)
Proposed Granted
AWARD NO.
ORGANIZATION
Stanford University
PRINCIPAL INVESTIGATOR / PROJECT DIRECTOR
Robert V Wagoner
A. SENIOR PERSONNEL: PI/PD, Co-PI’s, Faculty and Other Senior Associates
(List each separately with title, A.7. show number in brackets)
NSF Funded
Person-months
CAL
ACAD
1. Robert V Wagoner - Professor of Physics, Emeritus
3.00 0.00
2.
3.
4.
5.
6. ( 0 ) OTHERS (LIST INDIVIDUALLY ON BUDGET JUSTIFICATION PAGE)
0.00 0.00
7. ( 1 ) TOTAL SENIOR PERSONNEL (1 - 6)
3.00 0.00
B. OTHER PERSONNEL (SHOW NUMBERS IN BRACKETS)
1. ( 1 ) POST DOCTORAL ASSOCIATES
12.00 0.00
2. ( 2 ) OTHER PROFESSIONALS (TECHNICIAN, PROGRAMMER, ETC.)
2.40 0.00
3. ( 1 ) GRADUATE STUDENTS
4. ( 1 ) UNDERGRADUATE STUDENTS
5. ( 0 ) SECRETARIAL - CLERICAL (IF CHARGED DIRECTLY)
6. ( 0 ) OTHER
TOTAL SALARIES AND WAGES (A + B)
C. FRINGE BENEFITS (IF CHARGED AS DIRECT COSTS)
TOTAL SALARIES, WAGES AND FRINGE BENEFITS (A + B + C)
D. EQUIPMENT (LIST ITEM AND DOLLAR AMOUNT FOR EACH ITEM EXCEEDING $5,000.)
TOTAL EQUIPMENT
E. TRAVEL
1. DOMESTIC (INCL. CANADA, MEXICO AND U.S. POSSESSIONS)
2. FOREIGN
F. PARTICIPANT SUPPORT COSTS
0
1. STIPENDS
$
0
2. TRAVEL
0
3. SUBSISTENCE
0
4. OTHER
TOTAL NUMBER OF PARTICIPANTS
(
0)
G. OTHER DIRECT COSTS
1. MATERIALS AND SUPPLIES
2. PUBLICATION COSTS/DOCUMENTATION/DISSEMINATION
3. CONSULTANT SERVICES
4. COMPUTER SERVICES
5. SUBAWARDS
6. OTHER
TOTAL OTHER DIRECT COSTS
H. TOTAL DIRECT COSTS (A THROUGH G)
I. INDIRECT COSTS (F&A)(SPECIFY RATE AND BASE)
TOTAL PARTICIPANT COSTS
SUMR
Funds
Requested By
proposer
Funds
granted by NSF
(if different)
0.00 $
37,421 $
0.00
0.00
0
37,421
0.00
0.00
48,066
15,987
27,623
1,440
0
0
130,537
26,537
157,074
0
11,313
7,176
0
7,728
850
0
0
0
18,432
27,010
202,573
56.0% of MTDC as negotiated with cognizant fed agency (Rate: 56.0000, Base: 185141)
TOTAL INDIRECT COSTS (F&A)
103,679
J. TOTAL DIRECT AND INDIRECT COSTS (H + I)
306,252
K. RESIDUAL FUNDS (IF FOR FURTHER SUPPORT OF CURRENT PROJECTS SEE GPG II.C.6.j.)
0
L. AMOUNT OF THIS REQUEST (J) OR (J MINUS K)
$
306,252 $
M. COST SHARING PROPOSED LEVEL $
AGREED LEVEL IF DIFFERENT $
Not Shown
PI/PD NAME
FOR NSF USE ONLY
INDIRECT COST RATE VERIFICATION
Robert V Wagoner
Date Checked
Date Of Rate Sheet
Initials - ORG
ORG. REP. NAME*
Meredith o’connor
1 *ELECTRONIC SIGNATURES REQUIRED FOR REVISED BUDGET
SUMMARY
YEAR 2
PROPOSAL BUDGET
FOR NSF USE ONLY
PROPOSAL NO.
DURATION (months)
Proposed Granted
AWARD NO.
ORGANIZATION
Stanford University
PRINCIPAL INVESTIGATOR / PROJECT DIRECTOR
Robert V Wagoner
A. SENIOR PERSONNEL: PI/PD, Co-PI’s, Faculty and Other Senior Associates
(List each separately with title, A.7. show number in brackets)
NSF Funded
Person-months
CAL
ACAD
1. Robert V Wagoner - Professor of Physics, Emeritus
3.00 0.00
2.
3.
4.
5.
6. ( 0 ) OTHERS (LIST INDIVIDUALLY ON BUDGET JUSTIFICATION PAGE)
0.00 0.00
7. ( 1 ) TOTAL SENIOR PERSONNEL (1 - 6)
3.00 0.00
B. OTHER PERSONNEL (SHOW NUMBERS IN BRACKETS)
1. ( 2 ) POST DOCTORAL ASSOCIATES
18.00 0.00
2. ( 2 ) OTHER PROFESSIONALS (TECHNICIAN, PROGRAMMER, ETC.)
2.40 0.00
3. ( 1 ) GRADUATE STUDENTS
4. ( 1 ) UNDERGRADUATE STUDENTS
5. ( 0 ) SECRETARIAL - CLERICAL (IF CHARGED DIRECTLY)
6. ( 0 ) OTHER
TOTAL SALARIES AND WAGES (A + B)
C. FRINGE BENEFITS (IF CHARGED AS DIRECT COSTS)
TOTAL SALARIES, WAGES AND FRINGE BENEFITS (A + B + C)
D. EQUIPMENT (LIST ITEM AND DOLLAR AMOUNT FOR EACH ITEM EXCEEDING $5,000.)
SUMR
Funds
granted by NSF
(if different)
0.00 $
38,731 $
0.00
0.00
0
38,731
0.00
0.00
74,623
16,547
28,589
1,490
0
0
159,980
32,218
192,198
TOTAL EQUIPMENT
E. TRAVEL
1. DOMESTIC (INCL. CANADA, MEXICO AND U.S. POSSESSIONS)
2. FOREIGN
F. PARTICIPANT SUPPORT COSTS
0
1. STIPENDS
$
0
2. TRAVEL
0
3. SUBSISTENCE
0
4. OTHER
TOTAL NUMBER OF PARTICIPANTS
(
0)
G. OTHER DIRECT COSTS
1. MATERIALS AND SUPPLIES
2. PUBLICATION COSTS/DOCUMENTATION/DISSEMINATION
3. CONSULTANT SERVICES
4. COMPUTER SERVICES
5. SUBAWARDS
6. OTHER
TOTAL OTHER DIRECT COSTS
H. TOTAL DIRECT COSTS (A THROUGH G)
I. INDIRECT COSTS (F&A)(SPECIFY RATE AND BASE)
Funds
Requested By
proposer
TOTAL PARTICIPANT COSTS
0
8,469
0
0
3,969
850
0
0
0
19,129
23,948
224,615
56.0% Indirect Costs as negotiated with cognizant federal agency (Rate: 56.0000, Base: 206486)
TOTAL INDIRECT COSTS (F&A)
115,632
J. TOTAL DIRECT AND INDIRECT COSTS (H + I)
340,247
K. RESIDUAL FUNDS (IF FOR FURTHER SUPPORT OF CURRENT PROJECTS SEE GPG II.C.6.j.)
0
L. AMOUNT OF THIS REQUEST (J) OR (J MINUS K)
$
340,247 $
M. COST SHARING PROPOSED LEVEL $
AGREED LEVEL IF DIFFERENT $
Not Shown
PI/PD NAME
FOR NSF USE ONLY
INDIRECT COST RATE VERIFICATION
Robert V Wagoner
Date Checked
Date Of Rate Sheet
Initials - ORG
ORG. REP. NAME*
Meredith o’connor
2 *ELECTRONIC SIGNATURES REQUIRED FOR REVISED BUDGET
SUMMARY
YEAR 3
PROPOSAL BUDGET
FOR NSF USE ONLY
PROPOSAL NO.
DURATION (months)
Proposed Granted
AWARD NO.
ORGANIZATION
Stanford University
PRINCIPAL INVESTIGATOR / PROJECT DIRECTOR
Robert V Wagoner
A. SENIOR PERSONNEL: PI/PD, Co-PI’s, Faculty and Other Senior Associates
(List each separately with title, A.7. show number in brackets)
NSF Funded
Person-months
CAL
ACAD
1. Robert V Wagoner - Professor of Physics, Emeritus
3.00 0.00
2.
3.
4.
5.
6. ( 0 ) OTHERS (LIST INDIVIDUALLY ON BUDGET JUSTIFICATION PAGE)
0.00 0.00
7. ( 1 ) TOTAL SENIOR PERSONNEL (1 - 6)
3.00 0.00
B. OTHER PERSONNEL (SHOW NUMBERS IN BRACKETS)
1. ( 2 ) POST DOCTORAL ASSOCIATES
18.00 0.00
2. ( 2 ) OTHER PROFESSIONALS (TECHNICIAN, PROGRAMMER, ETC.)
2.40 0.00
3. ( 1 ) GRADUATE STUDENTS
4. ( 1 ) UNDERGRADUATE STUDENTS
5. ( 0 ) SECRETARIAL - CLERICAL (IF CHARGED DIRECTLY)
6. ( 0 ) OTHER
TOTAL SALARIES AND WAGES (A + B)
C. FRINGE BENEFITS (IF CHARGED AS DIRECT COSTS)
TOTAL SALARIES, WAGES AND FRINGE BENEFITS (A + B + C)
D. EQUIPMENT (LIST ITEM AND DOLLAR AMOUNT FOR EACH ITEM EXCEEDING $5,000.)
TOTAL EQUIPMENT
E. TRAVEL
1. DOMESTIC (INCL. CANADA, MEXICO AND U.S. POSSESSIONS)
2. FOREIGN
F. PARTICIPANT SUPPORT COSTS
0
1. STIPENDS
$
0
2. TRAVEL
0
3. SUBSISTENCE
0
4. OTHER
TOTAL NUMBER OF PARTICIPANTS
(
0)
G. OTHER DIRECT COSTS
1. MATERIALS AND SUPPLIES
2. PUBLICATION COSTS/DOCUMENTATION/DISSEMINATION
3. CONSULTANT SERVICES
4. COMPUTER SERVICES
5. SUBAWARDS
6. OTHER
TOTAL OTHER DIRECT COSTS
H. TOTAL DIRECT COSTS (A THROUGH G)
I. INDIRECT COSTS (F&A)(SPECIFY RATE AND BASE)
TOTAL PARTICIPANT COSTS
SUMR
Funds
Requested By
proposer
Funds
granted by NSF
(if different)
0.00 $
39,801 $
0.00
0.00
0
39,801
0.00
0.00
77,235
17,127
29,590
1,543
0
0
165,296
33,258
198,554
0
8,105
3,588
0
1,000
850
0
0
0
19,854
21,704
231,951
As negotiated with cognizant federal agency (Rate: 56.0000, Base: 213097)
TOTAL INDIRECT COSTS (F&A)
119,334
J. TOTAL DIRECT AND INDIRECT COSTS (H + I)
351,285
K. RESIDUAL FUNDS (IF FOR FURTHER SUPPORT OF CURRENT PROJECTS SEE GPG II.C.6.j.)
0
L. AMOUNT OF THIS REQUEST (J) OR (J MINUS K)
$
351,285 $
M. COST SHARING PROPOSED LEVEL $
AGREED LEVEL IF DIFFERENT $
Not Shown
PI/PD NAME
FOR NSF USE ONLY
INDIRECT COST RATE VERIFICATION
Robert V Wagoner
Date Checked
Date Of Rate Sheet
Initials - ORG
ORG. REP. NAME*
Meredith o’connor
3 *ELECTRONIC SIGNATURES REQUIRED FOR REVISED BUDGET
SUMMARY
Cumulative
FOR NSF USE ONLY
PROPOSAL BUDGET
ORGANIZATION
PROPOSAL NO.
Stanford University
PRINCIPAL INVESTIGATOR / PROJECT DIRECTOR
DURATION (months)
Proposed Granted
AWARD NO.
Robert V Wagoner
A. SENIOR PERSONNEL: PI/PD, Co-PI’s, Faculty and Other Senior Associates
(List each separately with title, A.7. show number in brackets)
NSF Funded
Person-months
CAL
ACAD
1. Robert V Wagoner - Professor of Physics, Emeritus
9.00 0.00
2.
3.
4.
5.
6. (
) OTHERS (LIST INDIVIDUALLY ON BUDGET JUSTIFICATION PAGE)
0.00 0.00
7. ( 1 ) TOTAL SENIOR PERSONNEL (1 - 6)
9.00 0.00
B. OTHER PERSONNEL (SHOW NUMBERS IN BRACKETS)
1. ( 5 ) POST DOCTORAL ASSOCIATES
48.00 0.00
2. ( 6 ) OTHER PROFESSIONALS (TECHNICIAN, PROGRAMMER, ETC.)
7.20 0.00
3. ( 3 ) GRADUATE STUDENTS
4. ( 3 ) UNDERGRADUATE STUDENTS
5. ( 0 ) SECRETARIAL - CLERICAL (IF CHARGED DIRECTLY)
6. ( 0 ) OTHER
TOTAL SALARIES AND WAGES (A + B)
C. FRINGE BENEFITS (IF CHARGED AS DIRECT COSTS)
TOTAL SALARIES, WAGES AND FRINGE BENEFITS (A + B + C)
D. EQUIPMENT (LIST ITEM AND DOLLAR AMOUNT FOR EACH ITEM EXCEEDING $5,000.)
TOTAL EQUIPMENT
E. TRAVEL
1. DOMESTIC (INCL. CANADA, MEXICO AND U.S. POSSESSIONS)
2. FOREIGN
F. PARTICIPANT SUPPORT COSTS
0
1. STIPENDS
$
0
2. TRAVEL
0
3. SUBSISTENCE
0
4. OTHER
TOTAL NUMBER OF PARTICIPANTS
(
0)
G. OTHER DIRECT COSTS
1. MATERIALS AND SUPPLIES
2. PUBLICATION COSTS/DOCUMENTATION/DISSEMINATION
3. CONSULTANT SERVICES
4. COMPUTER SERVICES
5. SUBAWARDS
6. OTHER
TOTAL OTHER DIRECT COSTS
H. TOTAL DIRECT COSTS (A THROUGH G)
I. INDIRECT COSTS (F&A)(SPECIFY RATE AND BASE)
TOTAL PARTICIPANT COSTS
SUMR
Funds
Requested By
proposer
Funds
granted by NSF
(if different)
0.00 $
115,953 $
0.00
0.00
0
115,953
0.00
0.00
199,924
49,661
85,802
4,473
0
0
455,813
92,013
547,826
0
27,887
10,764
0
12,697
2,550
0
0
0
57,415
72,662
659,139
TOTAL INDIRECT COSTS (F&A)
338,645
J. TOTAL DIRECT AND INDIRECT COSTS (H + I)
997,784
K. RESIDUAL FUNDS (IF FOR FURTHER SUPPORT OF CURRENT PROJECTS SEE GPG II.C.6.j.)
0
L. AMOUNT OF THIS REQUEST (J) OR (J MINUS K)
$
997,784 $
M. COST SHARING PROPOSED LEVEL $
AGREED LEVEL IF DIFFERENT $
Not Shown
PI/PD NAME
FOR NSF USE ONLY
INDIRECT COST RATE VERIFICATION
Robert V Wagoner
Date Checked
Date Of Rate Sheet
Initials - ORG
ORG. REP. NAME*
Meredith o’connor
C *ELECTRONIC SIGNATURES REQUIRED FOR REVISED BUDGET
BUDGET JUSTIFICATION
GRAVITATIONAL RADIATION FROM ACCRETING NEUTRON STAR X-RAY
SOURCES: MODELING AND LIGO DATA ANALYSIS
R. A. Wagoner, Professor of Physics, Emeritus, Principal Investigator
25% effort for 12 months; based on a full time rate of $12,086 per month current year.
N. A. Robertson, Physical Sciences Research Associate,
10% effort for 12 months; based on a full time rate of $7,704 per month current year.
B. Lantz, Physical Sciences Research Associate,
10% effort for 12 months; based on a full time rate of $5,205 per month current year.
One 100% FTE Postdoctoral Research Affiliate will conduct research during all three
years of the project; the estimate is based on a full time rate of $3881 per month during
the current year. A second Postdoctoral Research Affiliate, Wynn Ho, is expected to join
in Years 2 and 3 at 50% FTE.
One Contingent Employee (undergraduate student) will assist during the academic year;
Estimate is based on 23% FTE during Spring Quarter (April, May, June) at a first year
rate of $480/month.
One Graduate Student Research Assistant for 12 months at a 50% effort during academic
quarters and a 50% effort during summer Quarter; based on a full time rate of $13,382
per quarter current year.
Indirect cost and staff benefit rates are established in accordance with the federal
government’s office of Management and Budget (OMB) costing principles, Circular A21, Costs Principles for Higher Education. These rates are negotiated between Stanford
and the Office of Naval Research (ONR), which is the cognizant federal agency
overseeing the administration of sponsored agreements at Stanford. In this proposal we
have used the current negotiated rates as follows:
Indirect cost rate on-campus 56%
Regular Employees 30.50%
Postdoctoral Research Affiliate19.10%
Graduate RA/TA 3.40%
Contingent 8.90%
It is assumed that salaries will increase by an average of 3.5% on Oct. 1 of each year. It is
also assumed that most other expenses will increase at the rate 3% per year.
EXPENDABLES: Expendables include lab supplies, software, photocopies, and other
expendables directly benefiting the project. In Year 1, desktop computers will be
Budget Justification (continued)
provided for the Postdoctoral Associate and the graduate student. Another desktop
computer will be purchased in Year 2 for the 2nd Postdoc. Each computer is estimated to
cost $2969, not including tax, shipping or handling. (Computer estimate based on Dell
Precision Workstation 360 Minitower, 3.00 GHz, 1MB/800 HzFSB, 1 GB DDR400
SDRAM Memory, ECC with Keyboard, Dell Flat Panel monitor, Graphics card, boot
hard drive, floppy, Microsoft Windows XP, Mouse, CD/DVD). These computers will be
used to support the project, and will not be used for general purpose or administrative
use. Other expendables will include lab supplies, software, photocopies, shipping and
other expendable items directly benefiting the project. Estimates for Years 2 and 3 are
based on 2% of MTDC.
Year 1:
Desktop computers (2)
Expendables
Year 2:
Desktop computers (1)
Expendables
$5938
$1790
-------$7728
Year 3:
Expendables
$1000
-------$1000
$2969
$1000
-------$3969
REPORTS AND PUBLICATIONS: Page charges are in excess of $100 per page for the
scientific journals in which we publish. Current experience is that reports and publication
charges are approximately 1% of total annual research funding. Estimate for this project
is $850/year.
OTHER CHARGES:
Tuition for Graduate student (not included in MTDC):
Year 1 $17,432
Year 2 $18,129
Year 3 $18,854
Telecommunication costs are estimated at $1000 per year.
TRAVEL
Actual travel will depend on research results and new developments in the field. New
results are most rapidly communicated through oral presentations at conferences. Talks at
domestic conferences are usually presented by students. All travel is based on roundtrip
coach airfare, current per diem rates, and local transportation costs.
-2-
Budget Justification (continued)
Number of trips
Costs
TRAVEL
Trips to Caltech/LIGO for
consultations/reviews
(3 days each trip)
Year 1
Year 2 Year 3
Total
1
846
1
449
2141
Trips to MIT/LIGO for consultations
(3 days each trip)
1
1279
Trips to Hanford, WA for shift/site
support
(7 days each trip)
1
1553
1
1553
1
1553
4659
Trips to LSC meeting in Hanford, WA
(4 days each trip)
1
1171
1
1171
1
1171
3513
Trips to Livingston, LA for shift/site
support
(7 days each trip)
1
1462
1
1462
1
1462
4386
1
1144
2288
Trips to LSC meeting in Livingston, LA
(4 days each trip)
Trips to Baltimore conference (domestic)
(5 days each trip)
1
846
1279
1
1144
1
1905
Trips to GW, isolation and controls
conferences
(5 days each trip)
2
3858
Shared trip to GEO/Glasgow for
consultations
(7 days each trip)
2
7176
Total Travel 18,489
Foreign 7176
Domestic 11313
1
1929
8469
0
8469
1905
1
1929
7716
1
3588
10764
11693
3588
8105
38651
10764
27887
EQUIPMENT Desktop computers costing less than the $5000 equipment threshold will
be purchased for the Postdoctoral Associates and Graduate Student. See description
under Expendables.
-3-
Current and Pending Support
(See GPG Section II.D.8 for guidance on information to include on this form.)
The following information should be provided for each investigator and other senior personnel. Failure to provide this information may delay consideration of this proposal.
Other agencies (including NSF) to which this proposal has been/will be submitted.
Investigator: Robert Wagoner
Support:
Current
Pending
Submission Planned in Near Future
*Transfer of Support
Project/Proposal Title: Gravitational Radiation from Accreting Neutron Star X-ray
Sources: Modeling and LIGO Data Analysis (This
proposal)
NSF
Source of Support:
Total Award Amount: $
997,784 Total Award Period Covered: 09/01/05 - 08/31/08
Location of Project:
Stanford University
Person-Months Per Year Committed to the Project. Cal:3.00
Acad: 0.00 Sumr: 0.00
Support:
Current
Pending
Submission Planned in Near Future
*Transfer of Support
Project/Proposal Title:
Source of Support:
Total Award Amount: $
Total Award Period Covered:
Location of Project:
Person-Months Per Year Committed to the Project. Cal:
Acad:
Support:
Current
Pending
Submission Planned in Near Future
Sumr:
*Transfer of Support
Project/Proposal Title:
Source of Support:
Total Award Amount: $
Total Award Period Covered:
Location of Project:
Person-Months Per Year Committed to the Project. Cal:
Acad:
Support:
Current
Pending
Submission Planned in Near Future
Sumr:
*Transfer of Support
Project/Proposal Title:
Source of Support:
Total Award Amount: $
Total Award Period Covered:
Location of Project:
Person-Months Per Year Committed to the Project. Cal:
Acad:
Support:
Current
Pending
Submission Planned in Near Future
Sumr:
*Transfer of Support
Project/Proposal Title:
Source of Support:
Total Award Amount: $
Total Award Period Covered:
Location of Project:
Person-Months Per Year Committed to the Project. Cal:
Acad:
Summ:
*If this project has previously been funded by another agency, please list and furnish information for immediately preceding funding period.
Page G-1
USE ADDITIONAL SHEETS AS NECESSARY
Facilities, Equipment, and Other Resources
Laboratory:
The Kavli Institute of Particle Astrophysics and Cosmology (KIPAC) is an independent
laboratory located at Stanford University. KIPAC has offices in the Physics Department
as well as at the Stanford Linear Accelerator Center (SLAC), and laboratory space at both
locations. KIPAC is closely associated with the Hansen Experimental Physics
Laboratory and the Ginzton Laboratory, other Independent Laboratories at Stanford
participating in LIGO research. KIPAC has broken ground on a new facility at the
Stanford Linear Accelerator Center (SLAC), which is expected to be completed in 2007.
Computer:
In the Wagoner group at Stanford: Sun SPARCstation 5, Sun Ultra 10, and a Dell PC.
In the Kavli Institute of Particle Astrophysics and Cosmology (KIPAC): The PI will
have access to the new KIPAC computing resources. These are a dedicated compute
cluster with 20 processors, 50Gb of memory and 10Tb of disk space based on Apple
Xserve technology, and a large shared memory machine with 72 processors and 150 Gb
of memory and an additional 5Tb of fast disk space. The sophisticated algorithms to carry
out this research program will be developed on the shared memory machine and initially
can take advantage of the powerful yet simple parallelization strategy of OpenMP. Once
the algorithms are tested and optimized it will be worthwhile to write an MPI version that
will allow to take advantage of the cluster that is being expanded as well as some of the
existing large compute clusters at SLAC.
Office:
Because of the computational nature of this work, this project will be primarily utilize the
computing facilities available at KIPAC both at SLAC and on the Stanford campus.