Noise budget of LCGT

Off[General::"spell1"]
Off[General::"spell"]

hmirrorcoa[f_]=Import["hmirrorcoa.m"];
hmirrorstr[f_]=Import["hmirrorstr.m"];
hmirrorthermo[f_]=Import["hmirrorthermo.m"];
hmirror[f_]=Import["hmirror.m"];
hsusp[f_]=Import["hsuspYama.m"];
hseis[f_]=Import["hseis.m"];

SRM reflectivity (to be tuned)

ρ=0.86; (* SRM reflectivity *)

1.Parameters (for LCGT)

1.1 Physical constants

hb=1.05457266912510183 (10^(-34));(* reduced Planck constant (J*s) *)
ω0=1.8 (10^15);
c=2.99792458000000117`*^8;(* speed of light (m/s) *)
Ω=2 π f;
kB=1.38*10^(-23);(* Boltzmann's constant (J/K) *)
g=9.8;(* acceleration of the gravity (m/s^2) *)
Gravity=6.673*10^(-11);(* Gravitational constant (m^3/Kg/s^2) *)
solarmass=1.989*10^(30);(* mass of Sun (Kg) *)
Mpc=365.2422*24*60*60*c*3.26*10^6;(* 1 Mpc (m) *)

1.2 Laser

lambda=1064*10^(-9);(* wavelength (m) *)
P0= 75;(* power into interderometer(W)*)

1.3 Main cavity

l=3*10^3;(* length of cavity (m); maybe 2.7km *)
w0=3*10^(-2); (* beam radius at mirrors (m); can be 4.5 (a=12.5cm) ~ 5.4cm (a=15cm) *)

1.4 Interferometer (see 2.3.2)

Gpower=11;(* power recycling gain; used to be 11; can be 14 *)

1.6 Mirror

rho=4.0*10^3;(* density (kg/m^3) *)
radius=12.5*10^(-2);(* radius (m); used to be 12.5cm; can be 15cm *)
height=15*10^(-2);(* height (m) *)
mass= rho*Pi*radius^2*height;(* mass (kg) *)

2.Optical readout noise

2.1 Additional parameter settings

m=mass; (* test mass (kg) *)
L=l; (* arm length (m) *)
I0=P0*Gpower; (* incident power to the beamsplitter *)
ζ=π/2*(80/90); (* readout phase; largest signal at π/2; changed for dc readout *)

2.2 Basic equations for RSE

hSQL=(Sqrt[((8 hb)/(m (Ω^2) (L^2)))]);

Sh=((hSQL^2)/(2 κ))(((Abs[C11 Sin[ζ]+C21 Cos[ζ]])^2)+((Abs[C12 Sin[ζ]+C22 Cos[ζ]])^2)+((Abs[P12 Sin[ζ]+P22 Cos[ζ]])^2)+((Abs[P11 Sin[ζ]+P21 Cos[ζ]])^2)+((Abs[Q12 Sin[ζ]+Q22 Cos[ζ]])^2)+((Abs[Q11 Sin[ζ]+Q21 Cos[ζ]])^2)+((Abs[N11 Sin[ζ]+N21 Cos[ζ]])^2)+((Abs[N12 Sin[ζ]+N22 Cos[ζ]])^2)+(((Abs[M]*(Sqrt[Sadd])))^2))/((τ^2) ((Abs[D1 Sin[ζ]+D2 Cos[ζ]])^2));

M=1+(ρ^2)Exp[4 I β]-2ρ(Cos[2ϕ]+(κ/2)Sin[2ϕ])Exp[2 I β]+λSR ρ(-ρ Exp[2 I β]+Cos[2ϕ]+(κ/2)Sin[2ϕ])Exp[2 I β]+ϵ ρ(2((Cos[β])^2)(-ρ Exp[2 I β]+Cos[2ϕ])+(κ/2)(3+Exp[2 I β])Sin[2ϕ])Exp[2 I β];
C11=(Sqrt[1-λPD])((1+(ρ^2)) (Cos[2 ϕ]+(κ/2) Sin[2 ϕ])-2 ρ Cos[2 β]-(1/4)ϵ(-2(((1+Exp[2 I β]))^2)ρ+4(1+(ρ^2))((Cos[β])^2)Cos[2ϕ]+(3+Exp[2 I β])κ(1+(ρ^2))Sin[2 ϕ])+λSR(Exp[2 I β]ρ-(1/2)(1+(ρ^2))(Cos[2 ϕ]+(κ/2)Sin[2ϕ])));
C12=(Sqrt[1-λPD])(τ^2) ( -Sin[2 ϕ]-κ  ((Sin[ϕ])^2)+(1/2)ϵ Sin[ϕ]((3+Exp[2 I β])κ Sin[ϕ]+4 ((Cos[β])^2)Cos[ϕ])+(1/2)λSR(Sin[2ϕ]+κ ((Sin[ϕ])^2)));
C21=(Sqrt[1-λPD])(τ^2) (Sin[2 ϕ]-κ  ((Cos[ϕ])^2)+(1/2)ϵ Cos[ϕ]((3+Exp[2 I β])κ Cos[ϕ]+4 ((Cos[β])^2)Sin[ϕ])+(1/2)λSR(-Sin[2ϕ]+κ ((Cos[ϕ])^2))) ;
C22=C11;
D1=(Sqrt[1-λPD])(-(1+ρ Exp[2 I β]) Sin[ϕ]+(1/4)ϵ(3+ρ+2ρ Exp[4 I β]+(1+5ρ)Exp[2 I β])Sin[ϕ]+(1/2)λSR Exp[2 I β]ρ Sin[ϕ]);
D2=(Sqrt[1-λPD])(-(-1+ρ Exp[2 I β]) Cos[ϕ]+(1/4)ϵ(-3+ρ+2ρ Exp[4 I β]+(-1+5ρ)Exp[2 I β])Cos[ϕ]+(1/2)λSR Exp[2 I β]ρ Cos[ϕ]);
P11=(1/2)(Sqrt[1-λPD])(Sqrt[λSR])τ(-2ρ Exp[2 I β]+2Cos[2ϕ]+κ Sin[2ϕ]);
P12=-(Sqrt[1-λPD])(Sqrt[λSR])τ Sin[ϕ](2Cos[ϕ]+κ Sin[ϕ]);
P21=(Sqrt[1-λPD])(Sqrt[λSR])τ Cos[ϕ](2Sin[ϕ]-κ Cos[ϕ]);
P22=P11;
Q11=(Sqrt[λPD])(Exp[-2 I β]+(ρ^2)Exp[2 I β]-ρ(2 Cos[2ϕ]+κ Sin[2 ϕ])+(1/2)ϵ ρ(Exp[-2 I β]Cos[2ϕ]+Exp[2 I β](-2ρ-2ρ Cos[2 β]+Cos[2ϕ]+κ Sin[2ϕ])+2 Cos[2ϕ]+3 κ Sin[2ϕ])-(1/2)λSR ρ(2ρ Exp[2 I β]-2 Cos[2ϕ]-κ Sin[2ϕ]));
Q12=0;
Q21=0;
Q22=Q11;
N11=(Sqrt[1-λPD])(Sqrt[(ϵ/2)])τ(κ(1+ρ Exp[2 I β])Sin[ϕ]+2Cos[β](Exp[-I β]Cos[ϕ]-ρ Exp[I β](Cos[ϕ]+κ Sin[ϕ])));
N12=-(Sqrt[1-λPD])(Sqrt[2 ϵ])τ(Exp[-I β]+ρ Exp[I β])Cos[β]Sin[ϕ];
N22=-(Sqrt[1-λPD])(Sqrt[2 ϵ])τ(-Exp[-I β]+ρ Exp[I β])Cos[β]Cos[ϕ];
N21=(Sqrt[1-λPD])(Sqrt[(ϵ/2)])τ(-κ(1+ρ)Cos[ϕ]+2Cos[β](Exp[-I β]+ρ Exp[I β])Cos[β] Sin[ϕ]);

γ=T c/(4 L);(* cavity pole *)
τ=(Sqrt[1-(ρ^2)]); (* SRM transmittance *)
β=ArcTan[Ω/γ]; (* phase shift in the arm cavity *)
κ=((2 (I0/ISQL) (γ^4))/((Ω^2) ((γ^2)+(Ω^2)))); (* coefficient that shows how much the mirror moves *)
ISQL=((m (L^2) (γ^4))/(4 ω0)); (* the power with which the quantum noise reaches the SQL at the cavity pole frequency *)

2.3 Loss parameters

roundtriploss=70*10^(-6); (* ppm *)
ϵ = 2/T*roundtriploss; (* loss parameter of arms defined in KLMTV paper *)
λSR =0.02; (* loss in power at the signal recycling mirror *)
λPD=0.1;  (* 1 - PD's quantum efficiency in power *)
Sadd= 0*((π^2)/8 - 1); (* ((nonstationary shot noise)/(original shot noise))^2 ; SQW demod -> (π^2)/8 - 1, Sin-wave demod -> 0.5, optimized demod with 3rd harmonics -> 9(π^2)/80 - 1; 0 for DC readout  *)

3.Observable distance (Compact binary coalescense)

3.1 Parameters

m1=1.4*solarmass;(* mass of a compact object (Kg) *)
m2=1.4*solarmass;(* mass of other compace object (Kg) *)
mtotal=m1+m2;(* total moss of binary system (Kg) *)
mreduce=m1*m2/mtotal;(* reduced mass of binary system (Kg) *)
fmin=20;(* low cut off frequency of integral (Hz) *)
fmax=c^3/(6^(3/2)*Pi*Gravity*mtotal);(* high cut off frequency of integral (Hz) *)
SNR=10;(* threshold of Signal to Noise Ratio *)

3.2 Observable distance (Optimal case)

3.2.1 Integration

fmid=300;
Nini=60;
Nmid=20;

integ03=((∑_(ff=1)^Nini)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmid-fmin)/Nini/.f->fmin+(fmid-fmin)*(ff-0.5)/Nini)/.T->0.003)+((∑_(ff=1)^Nmid)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmax-fmid)/Nmid/.f->fmid+(fmax-fmid)*(ff-0.5)/Nmid)/.T->0.003);
integ04=((∑_(ff=1)^Nini)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmid-fmin)/Nini/.f->fmin+(fmid-fmin)*(ff-0.5)/Nini)/.T->0.004)+((∑_(ff=1)^Nmid)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmax-fmid)/Nmid/.f->fmid+(fmax-fmid)*(ff-0.5)/Nmid)/.T->0.004);
integ05=((∑_(ff=1)^Nini)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmid-fmin)/Nini/.f->fmin+(fmid-fmin)*(ff-0.5)/Nini)/.T->0.005)+((∑_(ff=1)^Nmid)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmax-fmid)/Nmid/.f->fmid+(fmax-fmid)*(ff-0.5)/Nmid)/.T->0.005);
integ06=((∑_(ff=1)^Nini)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmid-fmin)/Nini/.f->fmin+(fmid-fmin)*(ff-0.5)/Nini)/.T->0.006)+((∑_(ff=1)^Nmid)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmax-fmid)/Nmid/.f->fmid+(fmax-fmid)*(ff-0.5)/Nmid)/.T->0.006);
integ07=((∑_(ff=1)^Nini)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmid-fmin)/Nini/.f->fmin+(fmid-fmin)*(ff-0.5)/Nini)/.T->0.007)+((∑_(ff=1)^Nmid)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmax-fmid)/Nmid/.f->fmid+(fmax-fmid)*(ff-0.5)/Nmid)/.T->0.007);
integ08=((∑_(ff=1)^Nini)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmid-fmin)/Nini/.f->fmin+(fmid-fmin)*(ff-0.5)/Nini)/.T->0.008)+((∑_(ff=1)^Nmid)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmax-fmid)/Nmid/.f->fmid+(fmax-fmid)*(ff-0.5)/Nmid)/.T->0.008);
integ09=((∑_(ff=1)^Nini)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmid-fmin)/Nini/.f->fmin+(fmid-fmin)*(ff-0.5)/Nini)/.T->0.009)+((∑_(ff=1)^Nmid)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmax-fmid)/Nmid/.f->fmid+(fmax-fmid)*(ff-0.5)/Nmid)/.T->0.009);
integ10=((∑_(ff=1)^Nini)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmid-fmin)/Nini/.f->fmin+(fmid-fmin)*(ff-0.5)/Nini)/.T->0.010)+((∑_(ff=1)^Nmid)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmax-fmid)/Nmid/.f->fmid+(fmax-fmid)*(ff-0.5)/Nmid)/.T->0.010);
integ11=((∑_(ff=1)^Nini)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmid-fmin)/Nini/.f->fmin+(fmid-fmin)*(ff-0.5)/Nini)/.T->0.011)+((∑_(ff=1)^Nmid)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmax-fmid)/Nmid/.f->fmid+(fmax-fmid)*(ff-0.5)/Nmid)/.T->0.011);
integ12=((∑_(ff=1)^Nini)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmid-fmin)/Nini/.f->fmin+(fmid-fmin)*(ff-0.5)/Nini)/.T->0.012)+((∑_(ff=1)^Nmid)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmax-fmid)/Nmid/.f->fmid+(fmax-fmid)*(ff-0.5)/Nmid)/.T->0.012);
integ13=((∑_(ff=1)^Nini)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmid-fmin)/Nini/.f->fmin+(fmid-fmin)*(ff-0.5)/Nini)/.T->0.013)+((∑_(ff=1)^Nmid)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmax-fmid)/Nmid/.f->fmid+(fmax-fmid)*(ff-0.5)/Nmid)/.T->0.013);
integ14=((∑_(ff=1)^Nini)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmid-fmin)/Nini/.f->fmin+(fmid-fmin)*(ff-0.5)/Nini)/.T->0.014)+((∑_(ff=1)^Nmid)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmax-fmid)/Nmid/.f->fmid+(fmax-fmid)*(ff-0.5)/Nmid)/.T->0.014);

integ15=((∑_(ff=1)^Nini)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmid-fmin)/Nini/.f->fmin+(fmid-fmin)*(ff-0.5)/Nini)/.T->0.015)+((∑_(ff=1)^Nmid)(1/(f^(7/3)*(Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2))*(fmax-fmid)/Nmid/.f->fmid+(fmax-fmid)*(ff-0.5)/Nmid)/.T->0.015);

Pl03=LogLogPlot[integ03,{ϕ,0.05,π/2},PlotRange->All];
Pl04=LogLogPlot[integ04,{ϕ,0.05,π/2},PlotRange->All];
Pl05=LogLogPlot[integ05,{ϕ,0.05,π/2},PlotRange->All];
Pl06=LogLogPlot[integ06,{ϕ,0.05,π/2},PlotRange->All];
Pl07=LogLogPlot[integ07,{ϕ,0.05,π/2},PlotRange->All];
Pl08=LogLogPlot[integ08,{ϕ,0.05,π/2},PlotRange->All];
Pl09=LogLogPlot[integ09,{ϕ,0.05,π/2},PlotRange->All];
Pl10=LogLogPlot[integ10,{ϕ,0.05,π/2},PlotRange->All];
Pl11=LogLogPlot[integ11,{ϕ,0.05,π/2},PlotRange->All];
Pl12=LogLogPlot[integ12,{ϕ,0.05,π/2},PlotRange->All];
Pl13=LogLogPlot[integ13,{ϕ,0.05,π/2},PlotRange->All];
Pl14=LogLogPlot[integ14,{ϕ,0.05,π/2},PlotRange->All];

3.2.2 Changing T and ϕ

Show[Pl03,Pl04,Pl05,Pl06,Pl07,Pl08,Pl09,Pl10,Pl11,Pl12,Pl13,Pl14,PlotRange->All]

Square-root of the value above times 1.3*(10^(-20))is the observation distance in Mpc.

3.2.3 Optimal value for DRSE

Range15=FindMaximum[(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ15]/Mpc,{ϕ,1.0,1.6}]

Range14=FindMaximum[(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ14]/Mpc,{ϕ,1.0,1.6}]

Range13=FindMaximum[(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ13]/Mpc,{ϕ,1.0,1.6}]

Range12=FindMaximum[(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ12]/Mpc,{ϕ,1.0,1.6}]

Range11=FindMaximum[(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ11]/Mpc,{ϕ,1.0,1.6}]

Range10=FindMaximum[(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ10]/Mpc,{ϕ,1.0,1.6}]

Range09=FindMaximum[(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ09]/Mpc,{ϕ,1.0,1.6}]

Range08=FindMaximum[(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ08]/Mpc,{ϕ,1.0,1.6}]

Range07=FindMaximum[(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ07]/Mpc,{ϕ,1.0,1.6}]

Range06=FindMaximum[(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ06]/Mpc,{ϕ,1.0,1.6}]

Range05=FindMaximum[(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ05]/Mpc,{ϕ,1.0,1.6}]

Range04=FindMaximum[(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ04]/Mpc,{ϕ,1.0,1.6}]

Range14[[1]]==Max[Range14[[1]],Range13[[1]],Range12[[1]],Range11[[1]],Range10[[1]],Range09[[1]],Range08[[1]],Range07[[1]],Range06[[1]],Range05[[1]],Range04[[1]]]

Range14[[1]]
Range14[[2]][[1]]

We can see the optimal T and ϕ are T = 0.014 and ϕ = 1.124.

3.2.4 Optimal value for BRSE

RangeBRSE14=(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ14]/Mpc/.ϕ->π/2

RangeBRSE13=(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ13]/Mpc/.ϕ->π/2

RangeBRSE12=(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ12]/Mpc/.ϕ->π/2

RangeBRSE11=(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ11]/Mpc/.ϕ->π/2

RangeBRSE10=(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ10]/Mpc/.ϕ->π/2

RangeBRSE09=(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ09]/Mpc/.ϕ->π/2

RangeBRSE08=(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ08]/Mpc/.ϕ->π/2

RangeBRSE07=(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ07]/Mpc/.ϕ->π/2

RangeBRSE06=(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ06]/Mpc/.ϕ->π/2

RangeBRSE05=(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ05]/Mpc/.ϕ->π/2

RangeBRSE04=(1/SNR)/Sqrt[2]*2*(Gravity/c^3)^(5/6)*c*(5/96*mreduce)^(1/2)*(mtotal/Pi^2)^(1/3)*Sqrt[4*integ04]/Mpc/.ϕ->π/2

3.2.5 Optimal Result

PlotBRSE=LogLogPlot[(Sqrt[Sh])/.T->0.014/.ϕ->π/2,{f,1,(10^4)},PlotRange->{(1/(10^25)),(1/(10^20))},PlotStyle->Hue[0.1]];
PlotDRSE=LogLogPlot[(Sqrt[Sh])/.T->0.014/.ϕ->1.124,{f,1,(10^4)},PlotRange->{(1/(10^25)),(1/(10^20))},PlotStyle->Hue[0.5]];

4. Result with classical noise

P2=LogLogPlot[hsusp[f],{f,1,(10^4)},PlotRange->{(1/(10^25)),(1/(10^20))},PlotStyle->Hue[0.3]];
P3=LogLogPlot[hmirror[f],{f,1,(10^4)},PlotRange->{(1/(10^25)),(1/(10^20))},PlotStyle->Hue[0.7]];
P4=LogLogPlot[hseis[f],{f,1,(10^4)},PlotRange->{(1/(10^25)),(1/(10^20))},PlotStyle->Hue[0.9]];
PSQL=LogLogPlot[hSQL,{f,1,(10^4)},PlotRange->{(1/(10^25)),(1/(10^20))}];

Show[PlotBRSE,PlotDRSE,P2, P3, P4, PSQL]

PlotBRSEtotal=LogLogPlot[(Sqrt[Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2])/.T->0.014/.ϕ->π/2,{f,1,(10^4)},PlotRange->{(1/(10^25)),(1/(10^20))},PlotStyle->Hue[0.1]];
PlotDRSEtotal=LogLogPlot[(Sqrt[Sh+hsusp[f]^2+hmirror[f]^2+hseis[f]^2])/.T->0.014/.ϕ->1.124,{f,1,(10^4)},PlotRange->{(1/(10^25)),(1/(10^20))},PlotStyle->Hue[0.5]];

Show[PlotBRSEtotal,PlotDRSEtotal]

5. Contour Plot of T for DRSE and BRSE

listBRSE={{0.004,RangeBRSE04},{0.005,RangeBRSE05},{0.006,RangeBRSE06},{0.007,RangeBRSE07},{0.008,RangeBRSE08},{0.009,RangeBRSE09},{0.010,RangeBRSE10},{0.011,RangeBRSE11},{0.012,RangeBRSE12},{0.013,RangeBRSE13},{0.014,RangeBRSE14}};

listDRSE={{0.004,Range04[[1]]},{0.005,Range05[[1]]},{0.006,Range06[[1]]},{0.007,Range07[[1]]},{0.008,Range08[[1]]},{0.009,Range09[[1]]},{0.010,Range10[[1]]},{0.011,Range11[[1]]},{0.012,Range12[[1]]},{0.013,Range13[[1]]},{0.014,Range14[[1]]}};

ListLogPlot[{listBRSE,listDRSE},PlotRange->All]

Export["rho086BRSE.dat",listBRSE];
Export["rho086DRSE.dat",listDRSE];